The topology of collective leadership

a b s t r a c t

Over the past decade, there has been a surge of both theoretical and empirical research to
explore the possibilities of shared leadership, a reorientation of leadership away from
understanding the actions and interactions of “leaders” to understanding the emergent,
informal, and dynamic “leadership” brought about by the members of the collective itself.
Naturally, this focus on topology (or structural patterning) has prompted researchers to
leverage the advancements in network analytic methodology to understand this paradigm of
leadership. Despite the recognition of the unique advantage of studying collective leadership
using network analysis, there has been a translational gap. The current paper aims to fill this
gap, bridging the core ideas that epitomize collective leadership to the social network metrics
and analytics needed to fully understand its antecedents and consequences.

  1. Introduction
    The scientific study of leadership has long recognized that the behavior of leaders can have extraordinary effects on collectives
    including teams, units, and organizations (Kaiser, Hogan, & Craig, 2008). At the turn of this century, systematic inquiry into a new
    paradigm of leadership, dubbed shared leadership, took seriously the idea that the leadership responsible for these extraordinary
    effects could be attributed to the collective leading itself (Pearce & Conger, 2003). This paradigm reflects a shift in the focus of
    leadership research; from understanding the actions and interactions of “leaders” to understanding the emergent, informal, and
    dynamic “leadership” brought about by the members of the collective itself.
    Over the past decade, there has been a surge of both theoretical and empirical research to explore the possibilities of this new
    leadership paradigm (Denis, Langley, & Sergi, 2012; Friedrich, Vessey, Schuelke, Ruark, & Mumford, 2009). Much of that research
    has exploited the topology inherent in viewing leadership as an emergent, collectively enacted phenomenon. Naturally, this focus
    on topology (or structural patterning) has prompted researchers to leverage the advancements in network analytic methodology
    to understand this paradigm of leadership. Despite the recognition of the unique advantage of studying collective leadership
    using network analysis, there has been a translational gap. The current paper aims to fill this gap, bridging the core ideas that
    epitomize collective leadership to the social network metrics and analytics needed to fully understand its antecedents and
    consequences.
    We accomplish this in three parts. First, we integrate prior conceptual research on collective leadership, drawing out three
    structural aspects of collective leadership: people (i.e., leaders, followers, & their relations), roles (i.e., leadership functions), and
    time (i.e., dynamics). Second, we develop a bridging framework to enable these three dimensions to be fruitfully examined with
    network methodology. Third, we detail a range of metrics and analytic approaches that can be used to study these three core
    dimensions of collective leadership.

Although the core idea of collective leadership entered the scholarly discourse more than 60 years ago (Gibb, 1954), it was not
until the past decade that significant attention has been paid to understanding collective leadership (Pearce & Conger, 2003). In
contrast to the fifty-year period where the attention of leadership scholars was focused elsewhere on traits, behaviors, and the
like, the past 10 years has witnessed a flurry of energy and attention aimed at understanding collective leadership.
Pearce and Conger (2003) defined shared leadership “as a dynamic, interactive influence process among individuals in groups
for which the objective is to lead one another to the achievement of group or organizational goals or both (p. 1).” Pearce and
Conger went on to elaborate the structural nature of shared leadership, observing that leadership is “broadly distributed…instead
of centralized in the hands of a single individual (p. 1).” Cox, Pearce, and Perry (2003) called attention to the temporality inherent
in shared leadership, defining it as a “dynamic exchange of lateral influence (p. 48).” Fletcher and Käufer (2003) honed in on the
informal nature of shared leadership. Seers, Keller, and Wilkinson (2003) and Hiller, Day, and Vance (2006) have emphasized the
fact that collective leadership is a property of the group rooted in social exchange-based roles. Hiller and colleagues (2006) assert
that “the epicenter of collective leadership is… the interaction of team members to lead the team by sharing in leadership
responsibilities (p. 388).”
For the purpose of this review, we adopt the term “collective” leadership, which encompasses not only shared leadership but
also includes a variety of highly similar concepts (i.e., distributed and rotated leadership). In Table 1, we synthesize five works
that introduce important notions of the essence of collective leadership. These five works lay the groundwork for the model and
associated methodology presented here. The left half of Table 1 summarizes four key aspects of how collective leadership has
been defined in prior work: the conceptual definition, the focal unit of analysis, the informal nature of collective leadership, and
the essence of the leadership phenomena.
2.1. The forms of collective leadership: concentration
First, inherent in these works is the notion that multiple individuals are enacting leadership. Gronn (2002) discusses “one
individual, an aggregate of separate individuals, sets of small numbers of individuals (p. 428.)” Pearce and Conger (2003)
reference “individuals and groups (p. 1).” Hiller et al. (2006) discuss multiple “team members.” The fact that multiple individuals
are enacting leadership requires that we focus on the structural form as well as the intensity and direction of leadership
relationships.
Three papers have advanced our understanding of the forms of collective leadership. Mayo, Meindl, and Pastor (2003) were
the first to apply a social network approach to mapping collective leadership. Mayo and colleagues used two aspects of forms to
capture shared leadership: decentralization and density. Decentralization captures the distributed aspect of collective leadership.
Maximum decentralization occurs when leadership influence is evenly dispersed among all members of the collective. In contrast,
a centralized form of leadership occurs when the leadership influence is concentrated in one or very few members of the
collective. Mehra, Smith, Dixon, and Robertson (2006) also advanced our understanding of the topology of collective leadership
by describing four patterns of leadership: leader centered, distributed, distributed–coordinated, and distributed–fragmented.
Whereas Mayo et al. proposed the use of centralization and density metrics to capture leadership topology, Mehra qualitatively
coded observed leadership structures into the four types. Carson, Tesluk, and Marrone (2007) applied Mayo et al.’s approach,
using density as a metric reflecting the amount of shared leadership. In summary, there have been some efforts to describe the
topology of collective leadership networks. Further, the focus has been on capturing the extent to which the topology provides a
measure of the concentration of collective leadership in one or a handful of individuals.
2.2. The multiplexity of collective leadership: roles
The second aspect of collective leadership stems from the fact that leadership serves multiple collective functions or roles.
Mayo et al. (2003) used the transactional and transformational leadership framework, describing collective leadership as multiple
members of the group engaging in contingent reward, management by exception, charisma, individualized consideration, and
intellectual stimulation behaviors. Though Mayo et al. proposed the integration of transformational and transactional behaviors
with the collective leadership paradigm, empirical research has yet to utilize this framework. Empirical work has tested a
multidimensional framework, but a different one. Hiller et al. (2006) presented a four dimensional typology including: planning
and organizing, problem-solving, support and consideration, and developing and mentoring. Although Hiller and colleagues
expanded our view of the dimensionality of collective leadership, they failed to look at the structure. Rather, Hiller et al. captured
the amount of enactment of these four functions within teams, but did not model the pattern of who was enacting how much of
each of these functions with whom.
A role perspective lends itself well to understanding leadership activity in social groups. A role is defined as a dynamic set of
recurring behaviors, both expected and enacted, within a particular group context (Zigurs & Kozar, 1994). Thus, roles serve two
important functions by both establishing patterns for individual behavior through the interaction of members in a social unit
(Katz & Kahn, 1978), and also establishing expectations for the behaviors of others.
There is general agreement among scholars that leadership involves a complex of roles (e.g., Hollander, 1985), and a number
of scholars have offered theoretical typologies of the various roles or functions that leadership must provide within team settings.
While there has been no convergence on a single typology as preeminent, there is a surprising degree of overlap in the basic ideas

suggested by most of these scholars. Some of the earliest empirical work on team leadership points toward dual task and
relational leadership roles in teams. Bales (1950) and Bales and Slater (1955) studied emergent leadership in leaderless teams
and found that two leaders consistently emerged: the first was highly task-oriented (instrumental behaviors focused on assisting
the team in achieving its goals) while the second most influential was focused on the socio-emotional needs of the team
(reinforcing and guiding group behavior, inter-member relations, and group solidarity.) Hollander’s (1961) review of research on
emergent leadership also concluded that both task-focused (task competence and skill in coordination of team task goals) and
relational behaviors (skill in building trust) were important for individuals to be selected as leaders. More recent research has also
supported both task coordination behaviors and member support and development behaviors as being important for emergent
leadership in teams, with task behaviors being slightly more important (Kellett, Humphrey, & Sleeth, 2002; Taggar, Hackett, &
Saha, 1999).
Carson and Tesluk (2007) observed that there is a large degree of convergence around four distinct roles that are important for
team leadership (see Table 2): Navigator, Engineer, Social Integrator, and Liaison. The Navigator role enables the collective to
establish and maintain a clear purpose and direction. The Engineer role structures the collective and the task, coordinating the
contributions of members to meet the goals of the collective. The Social Integrator role maintains healthy and productive social
interactions and relational processes within the collective. Lastly, the Liaison role develops and maintains productive
relationships with key external stakeholders, serving as both an advocate and ambassador for the collective. We build on this
typology of roles to elaborate on how collective leadership can be tested with network analysis.
Seers et al. (2003) provide the most coherent theoretical elaboration to date to explain how multiple leadership roles
constitute collective leadership. Seers and colleagues define collective leadership as “the extent which more than one individual
can effectively operate in a distinctively influential role within the same interdependent role system (p. 79).” This definition
emphasizes that the multiple individuals enacting leadership are occupying different social roles, a view that builds on the early
work of Bales and colleagues (Bales, 1958; Bales & Slater, 1955) who observed that two individuals tend to emerge as leaders in
leaderless group discussions. The most respected expert occupies the “task leader” role, and the most liked member occupies the
“social leader” role. This role differentiation naturally occurs over the course of member interaction as “influence over others is
purchased at the price of allowing one’s self to be influenced by others (Homans, 1961, p. 286).” Seers and colleagues posit that
leadership differentiation, where members have little overlap in the focus of their leadership activities, benefits group
performance.
An alternative view is supported by research on the role of networks on collective action. Multiplexity in relationships, defined
as relations involving more than one type of relationship, result in more creative outcomes (Albrecht & Hall, 1991). Applied to
collective leadership, this view suggests that an advantage accrues to those collectives whose leadership ties carry more than one
type of leadership relationship. An example of this using the Hiller et al. framework is that teams where the individuals who are
setting direction are also developing and mentoring. The relative cost and benefits would seem to stem from the tradeoff between
specialization of labor versus coordination costs. Specialization in leadership roles allows particular individuals to focus on a
narrower scope of activities and to devote all of their attentional resources to those activities. However, specialization comes at a
cost to coordination across roles. There may be times when the planning and organizing role would be better enacted to
simultaneously consider the development and mentoring needs of the team. Having the same individuals influencing the same
others in both ways, i.e., leadership multiplexity, increases coordination across leadership functions.
The preceding discussion draws out the need to adequately test the impact of leadership multiplexity, as it is a core aspect of
collective leadership which has until now, received only scant attention. Thus far, we have explained that collective leadership
involves multiple individuals (i.e., forms) enacting multiple roles (i.e., multiplexity). We now turn to the third aspect of collective
leadership: time.
2.3. The dynamics of collective leadership: time
The third core aspect of collective leadership holds that multiple individuals enact multiple roles, and this topological
multiplexity (i.e., forms and role structure) changes over time. The importance of applying a temporal lens to the study of
collective leadership originates with the work of Pearce and Conger (2003), who observe that “individuals… can rise to the
occasion to exhibit leadership and then step back at other times to allow others to lead (p. 2).”
At the most basic level, incorporating time into collective leadership recognizes that a general leadership role is cycled among
different members of the collective. This is a variation on the vertical leadership form in that, at any given moment, the leadership
structure is hierarchical, top–down. However, the individual who enacts the hierarchical leadership role shifts over time.
Moreover, this form represents a structurally vertical form, but one in which the responsibility for leadership is shared
sequentially or serially among group members. An exemplar of this approach is Erez, LePine, and Elms (2002), who find that
rotation of leadership role allowed all team members to feel responsibility for the team’s success. They also reported that such
leadership increased the degree to which members offer suggestions for change in the team, and the overall level of cooperation
within the team. However, rotated leadership may reduce continuity over time, and this form may not always be matched to team
or task needs.
Accordingly, an extended view of the role of time was advanced by Friedrich et al. (2009), who advocate that “…collective
leadership is not static. As different problems emerge, different skills and expertise will be more appropriate (p. 935).”
As with many fields, the theoretical developments surrounding leadership as a collective phenomenon have progressed more
rapidly than have empirical findings. To date, the empirical studies examining the relationship between collective leadership and

group performance have shown mixed support, and have assessed the phenomena in multiple ways (e.g., Avolio, Jung, &
Sivasubramaniam, 1996; Carson et al., 2007; Carte, Chidambaram, & Becker, 2006; Ensley, Hmieleski, & Pearce, 2006; Hiller et al.,
2006; Mehra et al., 2006; Pearce, 1997; Pearce & Sims, 2002). In order to empirically validate theories of collective leadership, we
need more appropriate methodological linkages to the conceptualization of leadership as a phenomenon rooted in people, roles,
and time.
2.4. Operationalizing the topology of collective leadership
The preceding discussion illustrates that the three essential aspects of collective leadership theory are people, roles, and time.
In order to illustrate how we can use network analysis to appropriately model these three aspects of collective leadership, we
introduce a bridging framework depicted by the expression: LijRT. According to this model, L is leadership as viewed by member i
about member j. R is the leadership role: for instance, Navigator, Engineer, Social Integrator, and/or Liaison. And T is the time
period. Time could be conceptualized developmentally using team stages—forming, storming, norming, and performing
(Tuckman, 1965). Alternatively, time could be conceptualized using performance episodes (Marks, Mathieu, & Zaccaro, 2001). We
can understand collective leadership and the interplay among its components, i.e., people, roles, and time, using this integrated
model.
To begin, let us distinguish the two pure forms of leadership that have been articulated: vertical leadership and shared
simultaneous leadership. With vertical leadership, one person enacts all four leadership roles at all points in time. At the other
extreme, we have shared simultaneous leadership where all members of the team enact all of the leadership roles at all points in
time. These are likely to be artificial extremes of team leadership, with the leadership of most teams falling somewhere in
between. The LijRT model is offered as a way to formalize the range of possibilities of leadership arrangements that lie in between
these two extremes. The components of this model build on extant work on collective leadership that has considered multiple
people (Pearce & Sims, 2002), temporal rotation (Klein, Ziegert, Knight, & Xiao, 2006), and roles (Carson et al., 2007; Hiller et al.,
2006). Though these aspects of team leadership distribution have been advanced, we have lacked a coherent framework for
thinking about how these three dimensions of leadership forms result in a range of possible leadership arrangements. Formalizing
this model is a necessary first step to operationalizing collective leadership through networks. Let us next consider the LijRT model
of leadership in more detail.
According to this view, we can think of leadership in a team as represented by a three dimensional cube. We depict this cube in
Fig. 1. The x-axis of the cube depicts the leadership role. The y-axis of the cube depicts the team member. The z-axis of the cube
depicts meaningful units of time.
The three dimensions of collective leadership—member concentration, role multiplexity and temporal stability—can be
graphically described by filling in the section of the cube that depicts who on the team is enacting which leadership role at which
time point. In order to illustrate this view, we consider scenarios based on the two ends of the continuum on each of these
dimensions. In the case of member concentration, one end of the continuum is completely shared simultaneous leadership where
every member is enacting each of the four leadership roles at all time periods. In this case, the cube is completely full. This
leadership arrangement is depicted in Fig. 2, in the cell labeled A. At the other end of the continuum is a scenario when all roles of
leadership are concentrated across all points in time in just one individual. In this case, the cube has one flat horizontal slice
projecting into it. This situation is depicted in Fig. 2, in the cell labeled B.
The second dimension of collective leadership is role multiplexity. One end of the continuum on the role multiplexity
dimension describes a scenario where each individual enacts only a single leadership role. This is depicted in cell C of Fig. 2, where
each team member is only enacting leadership in one role. At the other end of this continuum is a scenario where a single
individual is enacting leadership in multiple roles. This is depicted in cell D of Fig. 2 where one team member, C, is taking on all
four leadership roles leading to high role multiplexity. This form of leadership is similar to Mehra et al.’s (2006) notion of
distributed leadership. It is noteworthy that cells B and D in Fig. 2 are identical but are being used to illustrate two distinct
characteristics of the collective leadership. As such the graphic in cells B and D, indicates a scenario where there is both high
member concentration and high role multiplexity.
The third dimension of collective leadership discussed in the literature is rotation, or its converse, which we label as temporal
stability. Imagine the scenario where the functions of leadership are being distributed to different individuals. So one individual is
enacting the Navigator role, another the Engineer role, another the Social Integrator role, and still another, the Liaison role. If there

is distribution across roles, but not across time, meaning each individual enacts the same role throughout time, then we would
have the leadership arrangement depicted in Fig. 2, in the cell labeled E. Here we essentially have four beams projecting into the
time dimension of the cube; each one at the position of a given member and their role. There is no rotation in roles among team
members over time. It is again worth noting that although the graphics in cells C and E are identical they represent one end of the
continuum on two different dimensions. As such, this graphic describes a scenario where the collective leadership has low role
multiplexity and low rotation (or high temporal stability). We can contrast this stable form of leadership to its dynamic
counterpart. In Fig. 2 cell F, we see the case of fully rotated leadership. Here, for instance, all four leadership roles as enacted by
team member D at Time 1, team member C at Time 2, team member B at Time 3, and team member A at Time 4.
Lastly, it is useful to depict the complexity that is possible by viewing combinations of these three aspects of collective
leadership: member concentration, role multiplexity, and temporal stability. Fig. 3 depicts a situation where leadership roles are
being enacted by different team members at different time points, and so the beams do not protrude all the way to the back of the
cube, rather they shift in location on the Y-axis corresponding to the members that are enacting the role at the new time point. It
is also important to note that each cell in the cube can include valued data about leadership roles, not simply a binary “yes/no”
about whether a particular person is enacting a particular role at a particular point in time. Using shades to indicate the extent of
role enactment can graphically depict this.
It is also informative to consider leadership arrangement using several two-dimensional projections of the cube. First, let us
consider a plot of people by role. These plots are generated at each meaningful time point in the team. Again, the meaningful time
point could be derived based on task cycles: transition and action phases (Marks et al., 2001), based on developmental stages:
forming, storming, norming, and performing (Tuckman, 1965), or based on important phase shifts such as the equilibrium shift
that occurs at the team midpoint (Gersick, 1989). We would have as many people by role plots as there are meaningful time
points. This plot conveys who in the team is enacting which leadership functional roles.
The second plot we would want to consider is a plot of people by time. This plot would convey who is serving as a leader for
the team at each meaningful time period. We would have four of these plots, one for each leadership role.
The third plot that we could consider is roles by time. In this case, we would have as many plots as there are individuals in the
team. So for each person, we are depicting the leadership roles that they are enacting, and the time at which they are enacting
them. This plot is especially valuable for examining how an individual’s leadership roles are changing over time.
In sum, what have previously been considered as distinct aspects of collective leadership, i.e., shared simultaneous, rotated,
distributed forms, can be well captured using this integrated model of leadership using these three planes to depict the three
dimensions of variations in aspects of leadership. We can now understand these three aspects of collective leadership—people,
roles, and time—as an integrated phenomenon.

  1. Collective leadership as networks
    In this section we describe how collective leadership can be characterized as particular configurations of social networks. A
    social network consists of a set of individuals and the relationships that bind them. There has been a modest but growing interest
    in applying a network perspective to leadership (Balkundi, Kilduff, & Harrison, 2011; Brass & Krackhardt, 1999; Hoppe & Reinelt,
    2010; Sparrowe, Liden, Wayne, & Kraimer, 2001). We extend this line of research by focusing specifically on applying a network
    perspective to collective leadership. Hence, we are interested in the leadership and influence relationships that bind a set of

individuals together, thereby regulating activity. In this way, collective leadership is a specific type of social network relation.
Other types of social network relations include friendship, advice, and hindrance ties (Brass, 1985; Cross, Borgatti, & Parker, 2001;
Lincoln & Miller, 1978). The leadership and influence network is then amenable to analysis using network analytic techniques
that both (a) describe the pattern of leadership activity in the collective, and (b) afford inferences about the antecedents and
consequences of these structural patterns of leadership.
The first step in using network analysis to study collective leadership is to define the collective and identify the members of it.
These individuals then constitute the nodes in the leadership network. The next step is to determine the leadership relations that
bind them. The two key decision points in using network analysis for the study of collective leadership are: elicitation and
structural representation (Mohammed, Klimoski, & Rentsch, 2000). Elicitation describes the content of the relational tie about
leadership. Elicitation of leadership networks can be accomplished using sociometric measures, i.e., “who leads whom” or “j as
perceived by i”, obtained via self-report, observation, or digital trace. Representation refers to the manner in which the structure
of relational ties about leadership is depicted. Mohammed et al.’s (2000) distinction between elicitation and representation is
particularly useful for thinking about collective leadership measures. Elicitation refers to the technique used to determine the
connections among individuals in the network (i.e., who is leading whom). Representation refers to the technique used to reveal
the structure of leadership.
3.1. Step 1: elicit leadership relations that make up the network
The first step in applying network methodology to the study of leadership is to elicit sociometric information about who is
leading whom. There are two important decision sets at this stage: elicitation method, and elicitation level. The elicitation method
describes the technique used to construct the leadership network. We detail two techniques: direct measurement and
unobtrusive measurement. The second decision is the level of analysis at which the technique is eliciting leadership networks,
and here we detail the distinction between leadership ties occurring at the person-to-person level versus those leadership ties
which connect a leader to a social entity. These are termed atomistic and molar views.
3.1.1. Elicitation method
The elicitation approach that most closely builds on current practice in leadership research is to elicit the network using direct
measures. Essentially, each person provides ratings of the leadership behavior of each other person. Table 3 presents examples of
prompts that can be used to elicit collective leadership. This basic approach was used by Carson et al. (2007) who asked
participants to rate each of his or her peers on the following question: “To what degree does your team rely on this individual for
leadership?” The molar section of Table 3 indicates an example of how Carson and Tesluk (2007) used a definition of each role
followed by a few sample behaviors to elicit leadership networks for each of the four leadership roles.
Because of the inherently psychological nature of leadership and influence, this elicitation approach maximizes the
psychological fidelity of the network, however it is extremely labor intensive for participants. A related approach is to use
observers, subject matter experts, to generate the leadership networks. This method is unobtrusive, but produces a network one
step away from the psychological meaning that would be revealed by asking the group members themselves.
An approach even further removed in terms of psychological fidelity, is to elicit the network using an unobtrusive source of
information. Relational information could be obtained by content coding a variety of unobtrusive sources of information including

participant observation, speech, texts, interviews, etc. and using this to construct the leadership network. This approach was used
recently using digital trace data.
Zhu, Kraut, and Kittur (2012, CSCW) used digital trace measures of shared leadership. Zhu et al. used an archival data source,
the posts left by Wikipedia contributors on other Wikipedia contributor’s profile page. Then they identified types of “leadership”
visible in these posts. For example, transactional leadership was reflected when one member rewarded another, and made it clear
that the reward was based on good performance by the other member. Aversive leadership was indicated if one member used a
set of strong negative words, including “block,” “revert” and “remove.” Raters first identified theoretically-meaningful coding
categories, then classified a set of Wikipedia posts into them identifying features such as the contingent reward language used to
capture transactional leadership, and then used machine learning (i.e., a computer codes a huge number of messages based on a
preset algorithm) to code more than four million messages for their leadership content.
3.1.2. Elicitation level
We distinguish between two elicitation levels for assessing leadership networks. These are: a) leadership ties occurring at the
person-to-person level; and b) those which connect a person (i.e., leader) to a social entity.
The first elicitation level, the person-to-person level, takes an atomistic perspective. Elicitation techniques such as sociometric
prompts that ask members of a collective questions such as “Who do you rely on for leadership?” elicit atomistic leadership
networks. The atomistic perspective is aligned with theories of leadership that acknowledge that leaders may have different
relationships with different people. For instance, theories of transformational leadership (Bass, 1998; Burns, 1978) have
acknowledged that leaders individualize their behaviors depending on the particular follower in question.
On the other hand, assessing leader-to-social entity (e.g., team, system, and organization) takes a molar perspective. From this
perspective, sociometric prompts identify individuals whom others perceive as leaders of the collective, not necessarily leaders of
the focal individual. For example, sociometric prompts such as “Who does your team rely on for leadership?” elicit molar
leadership networks. Prior work (e.g., Carson et al., 2007) has assessed shared team leadership using prompts that elicit these
molar networks.
Whereas in smaller collectives (e.g., 5-person teams) molar leadership prompts can be used to identify the degree to which
members are perceived by other members as leaders of the team as a whole, networks within this perspective may be more
difficult to interpret as the size of the collective increases. As the level of analysis increases, from teams to larger systems to entire
organizations, it may be much more difficult for individuals to accurately rate the degree to which the entire collective entity
relies on a given person for leadership. Taking an atomistic view, therefore, may be more appropriate for understanding
leadership in larger collectives.
Trace data can be either atomistic or molar, and it is important to distinguish these. Because Zhu et al.’s study used directed
interactions from “leaders” to “followers”, they are atomistic. On the other hand, digital trace data could capture molar leadership
if “leaders” address their communication to entire online communities. In this case, members of the community not only perceive
this information, but are aware that others are perceiving this information as well.
3.2. Step 2: represent the topological structure of the leadership network
While the previous section described the various strategies to elicit network data here we describe how these data are
represented. Let us re-consider the entry in each cell within the cube depicted in Fig. 1. Each cell captures the extent to which a
particular person exhibits leadership on a particular role during a specific time interval. However, it does not depict which
individuals perceived this person to demonstrate a certain level of leadership. As such, the cube only represents LjRT (the extent
to which an individual j was perceived to be a leader on a certain role, R, at a particular time, T) rather than LijRT (the extent to
which individual i perceived an individual j to be a leader on a certain role, R, at a particular time, T). Hence each entry in the cube
is itself computed from a structural representation of the overall LijRT leadership network.
The cube, as depicted in Fig. 2, is very appropriate to characterize collective leadership along the three dimensions of member
concentration, role multiplexity and rotation (or temporal stability). However, for analytic purposes it is necessary to explore
metrics that characterize collective leadership at higher levels of resolution than can be depicted in the cube. There are a suite of
“diversity” metrics that can be used to index the extent to which leadership roles are spread across people and time in the cube.
These include Shannon’s (1948) information theoretic measure, H, of entropy, and the Gibbs–Martin index (Gibbs & Martin,
1962) more commonly known as the Blau index. These single measure diversity indices would take on higher values if there were
lower member concentration (diverse set of individuals are leaders), lower role multiplexity (diverse set of individuals are
enacting different roles) and lower temporal stability (diverse set of individuals are enacting leadership roles at different points in
time).
While these single measure indices can be useful to gain a more nuanced characterization of the collective leadership
prevalent in the team, one can compute additional metrics based on the overall LijRT network at the actor, dyadic, triadic,
subgroup, and overall network level. It is important to make a distinction between the more common use of the term “level” in
organizational studies from how the term is sometimes invoked in network analysis. In organizational studies, the term level of
analysis is used, for instance, to describe the level of the outcome variable, which could be, for instance, at the individual, group, or
organizational level. In network analysis, the term “level” is often used to describe the locus of the emergent phenomena
(Contractor, Wasserman, & Faust, 2006). More specifically, in the remainder of this section we explore how we can characterize
the three dimensions of collective leadership based on network metrics computed at the (i) actor level (such as the number of

times an actor is cited as a leader by other in the network), (ii) dyad level (the pairwise similarity between actor’s leadership ties),
(iii) triad level (the presence of a leadership hierarchy among individuals taken three at a time), (iv) group level (the presence of
a core group of leaders) and (v) network level (the overall level of leadership centralization). Table 4 presents an overview of
these metrics, and depicts the connection between the three dimensions of collective leadership: member concentration, role
multiplexity, and temporal stability and each of these metrics at each level of analysis.
3.2.1. Actor (individual) level
In network parlance, actor level measures refer to network metrics that are computed for each actor (in our case, individual) in
the network. One of the simplest, and most intuitive, actor level measures is in-degree centrality. An individual i’s in-degree
centrality is defined as the strength and number of links received from other individuals. Hence an individual i’s role leadership is
the extent to which other individuals, j, rate i (say, on a scale of 1 to 5) as providing leadership in a particular role (for instance, as
a navigator, engineer, social integrator, or liaison) during a given time period. The presence of a few individuals with high role
leadership scores would reflect a high concentration in the collective leadership. This in-degree measure of role leadership is what
gets entered into the various cells within the cube describe above and depicted in Fig. 1. A darker shade or black in a particular cell
indicates that a person was widely perceived as a leader for a particular role during a given time interval.
Role leadership could be cumulated across roles. The measure of an individual i’s multi-role leadership is the extent to which
other individuals, j, rate i as providing leadership in all of the four roles during a given time period. The presence of individuals
with high multi-role leadership scores would indicate high role multiplexity in the collective leadership. An individual who scores
high on multi-role leadership is represented by a horizontal beam in the cube in Fig. 1.
Finally, an individual’s role (or multi-role) leadership can also be cumulated over time. The measure of an individual’s
sustained role (or multi-role) leadership is the extent to which other individuals, j, rate i as providing leadership on each (or all of
the four roles) across all time periods. The presence of individuals with high sustained role (or multi-role) leadership scores
would indicate stability in the collective leadership. A beam that is piercing into the cube (Fig. 1) represents an individual who
scores high on sustained (single) role leadership. A horizontal slice in the cube (Fig. 1) represents an individual who scores high
on sustained multi-role leadership.
3.2.2. Dyadic level
Dyadic level measures refer to network metrics that are computed for pairs of actors in the network. Structural equivalence is
one such dyadic measure (Burt, 1987). It can be used to measure the extent to which two individuals rate (or are rated) similarly
by all other individuals in the network in terms of their leadership on a specific role during a given time period. It is most
commonly computed as a standardized Euclidean distance or a Pearson correlation (Faust, 1988). The presence of only a handful
of structurally equivalent leaders for a particular role would indicate concentration in the collective leadership. It would also
indicate congruence in individual’s perception of the concentration in collective leadership.
Structural equivalence can also be computed across roles. It can be used to measure the extent to which two individuals are
rated similarly by all other individuals in the network in terms of their leadership across all four roles during a given time period.
The presence of only a handful of structurally equivalent leaders across roles would indicate role multiplexity in the collective
leadership.
Finally, structural equivalence could also be computed across time. That is, it can be used to measure the extent to which two
individuals are rated similarly by all other individuals in the network in terms of the leadership for each (or across all four) of the
roles across all time periods. The presence of only a handful of structurally equivalent leaders for a particular role (or over all four
roles) across all time periods would indicate stability in the collective leadership.
3.2.3. Triadic level
Triadic level network measures are computed for sets of three actors and the relations among them. Transitivity is one
commonly used triadic measure. A triad is defined as transitive if for a specific role in a given time period, actor i selects actor j,

actor j selects actor k, and actor i selects actor k (Holland & Leinhardt, 1971). A transitive triad signals a concentration in
leadership, in this case, in actor k. Transitivity of a network is defined as the number of transitive triads as a ratio of all the possible
triads in the network. Hence it follows, that a leadership network with high transitivity for a specific role in a given time would
indicate concentration in the collective leadership.
Transitivity can also be computed across roles. In this case the triad is defined as transitive if for a given time actor i selects
actor j, actor j selects actor k, and actor i selects actor k on any or all of the four leadership roles. A leadership network with high
transitivity across roles would indicate role multiplexity in the collective leadership.
Finally, transitivity can be computed across time. In this case the triad is defined as transitive if actor i selects actor j, actor j
selects actor k, and actor i selects actor k on any or all of the four leadership roles in all of the time periods. A leadership network
with high transitivity across time for any or all four of the leadership roles would indicate stability in the collective leadership.
3.2.4. Group level
Network analysis can also be used to identify a group of actors within the network that share some common structural
property. One such measure is a k-core (Hanneman & Riddle, 2005). A k-core is the largest group of actors, all of whom are
selected by some number (k) of other members of the group as providing leadership on a specific role for a given period of time.
As such, the k-core represents the set of individuals who are most frequently identified as leaders on a specific role for a given
time period. For any given group, as k (the number of individuals required to select a leader) increases the size of the k-core will
decrease. For instance, if k is chosen so as to represent 75% of the group, the number of individuals in the k-core is likely to be far
fewer than if k was chosen to represent 25% of the group.
The membership of the k-core can also be computed across roles. In this case the k-core is the largest group of actors, all of
whom are selected by some number (k) of other members of the group as providing leadership on two or more of the four specific
roles for a given period of time. For a given k, a large number of members in the k-core would indicate higher prevalence of role
multiplexity in the collective leadership.
Finally, membership of the k-core can be cumulated across time. In this case that the k-core is the largest group of actors, all of
whom are selected by some number (k) of other members of the group as providing leadership on two or more of the specific
roles at two or more of the given time periods. In this case, for a given k, a large number of members in the k-core would indicate
stability in the collective leadership.
3.2.5. Network level
Our progression up the levels of analysis from the actor to the dyad, to the triad, and to the group culminates at the overall
network level. The centralization of the network is one useful measure to characterize collective leadership. This measure,
computed at the network level, is based upon the actor level measure of in-degree centrality discussed earlier. A network has a
high level of in-degree centralization if one or a few of the actors have high in-degree centrality, while others have relatively low
in degree centrality. Networks often demonstrate such a pattern giving rise to so-called scale-free networks where proverbially
80% of the network ties are directed at 20% of the nodes (Barabasi & Albert, 1999). One commonly used measure is in-degree
network centralization (Freeman, 1977). It benchmarks the variability in the centrality among actors of the observed network to a
star network where one actor receives links from all other actors and none of the other actors receive any incoming links. More
specifically, in-degree network centralization is computed as the ratio of the variance in the in-degree centrality scores of the
actors in the observed network to the variance that would be found in a star network of the same size. A high in-degree
centralization score for a specific role leadership network at a given time period, would indicate that one or a few individuals
were identified as leaders for that role. As such it is a measure of concentration in the collective leadership.
As in the previous cases, in-degree network centralization could be computed based on actor’s in-degree centrality scores in
the multi-role leadership network at a given time period. In this case, high in-degree network centralization would indicate that
one or a few individuals were identified as leaders across multiple roles thereby reflecting high role-multiplexity in the collective
leadership.
Finally, in-degree network centralization could be computed based on actor’s in-degree centrality scores across one or more of
the four roles and across all time periods. Here, high in-degree network centralization would suggest that one or a few individuals
were identified as leaders on one or more of the roles consistently across all time periods, thereby reflecting stability in the
collective leadership.

  1. Using inferential network models to explain the antecedents and consequences of collective leadership
    Until recently, most research on leadership from a network perspective, like most network research in general, has been
    descriptive in nature. That is, network metrics are computed to characterize certain qualities of the network at the actor, dyadic,
    triadic, group or network level. In the preceding section, we considered metrics that would be particularly appropriate for the
    study of collective leadership. As in other methodological approaches, the descriptive metrics serve a useful purpose in
    characterizing the underlying data.
    While computing descriptive metrics are a necessary starting point in our analytic journey, it is often not the destination.
    Instead these measures can serve as the basis for asking and testing multi-theoretical and multilevel explanations for the
    emergence and outcomes of collective leadership. For instance, at the actor level we might seek to understand why a particular
    individual is more or less likely to be perceived as serving a specific leadership role. These explanations might include attributes of

the actor such as their gender or formal hierarchical level. It could also include relational measures such as their in degree
centrality. At the dyadic level, we might want to explain why pairs of individuals are more or less likely to perceive one another as
serving a certain leadership role. Likewise, at the triadic level, we might choose to theorize the extent to which the triads in which
they are embedded influence individuals’ ‘perceptions of others’ leadership roles. Moving up to the group level, we might
consider the extent to which cohesive subgroups (or, say, teams within multi-team systems) might influence perceptions of
leadership. At the network level, we can assess the extent to which global network characteristics might influence individuals’
perceptions of others’ leadership in a specific role. Finally, we might want to determine if the explanations for the emergence of
leadership roles are different for high performing teams versus low performing teams.
In all of these examples, with the exception of actors’ attributes (such as gender and formal hierarchical level), we seek to
explain the extent to which an individual perceives another as serving a specific leadership role based upon other individuals’
perceptions of who else serves in that same leadership role. As such, it seeks to explain endogenously, the emergence of, say, a
specific navigator leadership tie, based upon all other navigator leadership types in the network. The use of the term
“endogenous” here refers to the fact that we seek to explain the presence of a tie (on, say, navigation leadership) between actor i
and j based on the presence or absence of the same (hence, endogenous) type of tie (navigation leadership) among other actors in
the network. In addition to endogenous influences, we may seek to explore the emergence of a specific navigator leadership tie
based upon other exogenous relations such as other forms of leadership ties (e.g. social integrator, liaison, and engineer), other
network ties (such as trust), or the same leadership tie at a previous point in time. Clearly, these represent rich possibilities for
building and testing theories for the emergence and outcomes of leadership ties. But there is a reason why we have not seen such
questions addressed in the research literature.
Until recently, the most common way in which researchers—including those studying leadership—had tested network related
hypotheses is by computing network metrics at the level of the individual actor and using it as an explanatory or dependent
variable in traditional statistical techniques such as ANOVA or regression. However, in most cases these approaches disregard the
fact that network data and the metrics computed using them violate the independence assumption central to these statistical
techniques. Most traditional statistical techniques assume that the observations represent collection of random variables that are
independent and identically distributed (i.i.d.). This is patently not the case for network data where one observation (i.e., a
network link between two individuals A and B) cannot be assumed to be independent of another observation (i.e., a network link
between A and C or between B and C). In the past decade there has been considerable progress in the development of inferential
statistical techniques that overcome this limitation. These new approaches, described next, will strengthen the validity of
research findings in the area of leadership networks. They will also catalyze the consideration of multi-theoretical multilevel
explanations, such as those illustrated above, which go beyond the individual level metrics most often utilized in current research
on leadership from a network perspective.
Developing a statistical model of social networks requires a framework that accounts for the intrinsic interdependencies in
network data. Over the past 15 years, a class of statistical models called p* or exponential random graph models (ERGM) have
been developed which explicitly incorporate dependence assumptions for network analysis (Anderson, Wasserman, & Crouch,
1999; Frank, 1981; Frank & Strauss, 1986; Pattison &Wasserman, 1999; Robins, Pattison, Kalish, & Lusher, 2007; Robins, Pattison,
& Wasserman, 1999; Wasserman & Faust, 1994; Wasserman & Pattison, 1996; Wasserman & Robins, 2005). The basic premise of
these models is that any theoretical explanation for the emergence of leadership ties can be represented as a specific structural
signature. For instance, let us suppose we were to hypothesize that individuals are more likely to perceive someone within their
own unit, rather than in another unit, as serving a leadership role. We can describe this mechanism in terms of the structural
signatures shown below. The one on the left indicates two individuals who belong to the same unit (both the nodes are shaded).
The structural signature on the right indicates individuals who belong to different units. Based on our hypothesis, we would
expect greater likelihood of seeing leadership ties as described by the structural signature in Fig. 4A than in Fig. 4B. As another
example, suppose we were to hypothesize that if individual i rated individual j as a leader, it is unlikely that the ratee, individual j
would in turn rate individual i as a leader on the same role. In this case, we are positing that the structural signature shown in
Fig. 4C is very unlikely to occur in the leadership network.
While the structural signatures described above are fairly simple, the same approach can be used to define more sophisticated
structural signatures that would represent the three dimensions we used earlier in this study to characterize collective
leadership: member concentration, role multiplexity, and temporal stability. For instance, one commonly studied structural
signature, called k-star, is the likelihood that there are a few nodes (consider these as stars) in the network that are cited as
leaders by many others while the majority of nodes are cited as leaders by none or only a few. This is clearly a structural signature
that would characterize the member concentration dimension of collective leadership. While one might expect to find a few
nodes that receive more links than others even in a random network, the strength of the p*/ERGM approach is to statistically
confirm if the extent to which there are a few stars in the network is more than would be expected by chance. Another commonly
used structural signature, called multiplexity, assesses the extent to which two different relations appear together between pairs

of actors. An example would be if individuals would frequently cite the same other individuals as a leader based both on the
navigator role and social integrator role. As the name implies, this structural signature is clearly of relevance in characterizing the
role multiplexity dimension of collective leadership. Here again we would expect a certain amount of multiplexity (the
co-occurrence of two types of relations between pairs of actors) to occur even in a random network. The p/ERGM approach assesses the extent to which the observed multiplexity is, ceteris paribus, more than would be expected by chance. Finally, one can consider temporal structural signatures in longitudinal networks. Here we consider the case where we have individuals citing others’ leadership roles at multiple points in time. A temporal structural signature is one where the configuration of ties at one point in time influences the configuration of ties at a subsequent point in time. For instance, if i cites j as a leader and j cites k as a leader at one point in time, how likely is it that i will cite k as a leader at a subsequent point in time? The extent to which these changes occur would signal a lack of temporal stability in the collective leadership. The techniques to statistically infer the extent of temporal stability (or lack thereof) in longitudinal networks rely on longitudinal extensions to p/ERGMs (Wang, Robins, &
Pattison, 2006) as well as the statistically related stochastic actor-oriented models to study coevolution of networks (Steglich,
Snijders, & Pearson, 2010).
Once the structural signatures are theoretically specified, the next step is to count the frequency of the hypothesized structural
signatures in the observed network. That is, for instance in the above example, we compute how frequently we observe
leadership ties between two nodes belonging to the same units. The next question is to assess whether the frequency with which
we observe these structural signatures are above or below what we might expect by chance. In order to do this, we need to
generate a distribution of networks and then compare the frequency of the hypothesized structural signatures in the observed
network with the frequency of these structural signatures in the distribution of generated networks. The general form of the class
of (homogeneous) exponential random graph models used to create this distribution of networks is as follows:

where:
(i) the summation is over structural signatures of type A;
(ii) λA is the parameter corresponding to structural signatures of type A;
(iii) zA(x) is the network statistic (or frequency) corresponding to structural signature A
(iv) κ is a normalizing quantity to ensure that (1) is a proper probability distribution.
The model represents a probability distribution of networks on a fixed node set, where the probability of observing a network
depends on the presence of the various structural signatures hypothesized in the model. One can interpret the structure of a typical
network in this distribution as the result of cumulating these particular structural signatures. The estimated parameters provide
information about the presence of those structural signatures in the observed network (Robins, Snijders,Wang, Handcock, & Pattison,
2007). In essence, p/ERGM analyses test the likelihood for the theoretically hypothesized structural signatures to occur in the observed network thus reflecting the underlying social processes that generate the emergence of leadership (Robins et al., 2007; Shumate & Palazzolo, 2010). In summary, p/ERGMs allow us to test the hypotheses about the network without losing—and indeed leveraging—information
about interdependencies among relations by estimating the probabilities that the hypothesized structural signatures are observed
more (or less) frequently than by chance. In an exponential randomgraphmodel, the range of possible networks and their probability
of occurrence under the model are represented by a probability distribution on this set of all possible networks. The model is
constructed by specifying parameters corresponding to the structural signatures(s), which are more (or less) likely to occur in the
distribution. There are numerous structural tendencies to characterize these networks and the particular signatures tested must be
theoretically deduced. In the case of collective leadership they would correspond to member concentration, role multiplexity, and
stability. These structural signatures, in turn, can be interpreted within a multi-theoretical framework that accounts for various
endogenous and exogenous processes occurring at multiple levels of analysis that potentially govern the evolution of the network
(Contractor et al., 2006; Monge & Contractor, 2003).
The discussion thus far has focused on testing hypotheses about factors (at the actor, dyad, triad, subgroup, and network levels) that
influencemember concentration, rolemultiplexity, and stability of collective leadership. There is clearlymerit in understanding how, for
instance, the attributes of an actor (such as their tenure within the organization) influence their perception of the extent to which they
consider their peers taking on leadership roles. Likewise, at the dyadic level, it is theoretically interesting to understand how an actor’s
perception off another’s leadership is shaped by other dyadic relationships such as trust from one actor to another. However, in addition
to advancing our understanding of the antecedents to collective leadership, there is considerable interest in investigating the outcomes of
collective leadership, in terms of, say, performance and satisfaction. For instance, we might want to understand the extent to which
characteristics of collective leadership—member concentration, rolemultiplexity, and stability—influence, the performance of the group.
While the antecedents of collective leadership can be investigated by studying a single collective (team, department, multi-team
system, or organization), exploring the outcomes of collective leadership would need to investigate multiple collectives. This is
becausewe seek to explain the variance in outcomes based upon actor, dyad, triad, subgroup, and network level structural signatures
in each of the collectives.Hence in order to explore the impact of the three facets of collective leadership—member concentration, role
multiplexity, and stability—on the outcomes of collectives, the unit of analysis would have to be the collective. Following the collection
of data from multiple collectives, exploring the impact of collective leadership on outcome would require a two-part analytic strategy.

First, we would conduct the aforementioned p/ERGM analysis on each of the collectives. These analyses provide us with parameter estimates that reflect the extent to which specific structural signatures (at the actor, dyad, triad, etc. levels) characterize the collective leadership in each of the collectives. The next step is to explore the extent to which these structural signatures, which characterize the collective leadership in each of the collectives, can explain the variance in the outcome measures for each of these collectives. If the outcome measure is binary (failure vs. success) or ordinal (low versus medium versus high performance), one can conduct an ANOVA where the parameter estimates for the structural signatures serve as the explanatory variables. If, on the other hand, the outcome measures are continuous (e.g., level of performance and time to completion), one can conduct a regression or a path analysis where, once again the parameter estimates for the structural signatures in each collective serve as the explanatory variables. As an illustration, consideringmember concentration, substantive thinking holds that there are at least four advantages to teams with less concentrated (highly dispersed) leadership structures (Cox et al., 2003). These teams are thought to benefit from greater member engagement and enhanced coordination as members come to understand the nature of their interdependencies. Greater dispersion in leadership provides teams access to more ideas and information that may well translate into higher creativity and innovation. Finally, greater involvement in leadership by more members increases the task meaningfulness. An alternative possibility is that greater dispersion in leadership may well come at a cost to coordination, conflict, and effort (i.e., owing to free-riding). As mentioned earlier, k-star is a structural signature that indexes the extent towhich there is a highmember concentration (the presence of a few stars) in the leadership network. Our p/ERGManalyseswill provide uswith estimates of the k-star parameter for each collective. A large, positive and
statistically significant value for the parameter estimate would indicate the prevalence of stars in that collective more than one would
expect by chance. In order to empirically test the hypothesis that high member concentration leads to lower performance, we use
appropriate analytic techniques (such as ANOVA, regression or path analysis) where the k-star parameter estimated for each of the
collectives is the explanatory variable and the performance measure for each of the collectives is the outcome variable.
Additionally, onemight posit that the rolemultiplexity dimension of collective leadershipwill lead to the generation ofmore creative
ideas. Albrecht and her colleagues (Albrecht &Hall, 1991; Albrecht & Ropp, 1984) showthat individuals are only likely to discuss creative
(or innovative) ideas with those with whom they have both strong work and social ties. This is because discussions about innovative
ideas require both a certain measure of familiarity on task related issues as well as a level of trust as one explores under-developed ideas.
Based on this line of reasoningwemight posit that collectives where individuals rely on the same set of leaders formultiplex rolesmight
nurture the development ofmore innovative ideas than collectiveswith lowermultiplexity. To test this hypothesis,we begin by using
p/ERGM techniques to estimate the multiplexity parameter (described above) for each collective. A large, positive and statistically significant estimate for this parameter would indicate that this collective has a higher level of role multiplexity in its collective leadership than onewould expect by chance. As in the case described above formember concentration,we can use these estimates as explanatory variables to test their influence on the outcome variable, which in this case would be team creativity. For a final illustration, let us consider temporal stability. Prior research offers two ways to think about the impact of dynamic leadership structures on performance. The first notion suggests that as collective needs change, moving from exploration to exploitation and back, effective collectives are those that can shift their relative level of role enactment initially focusing on liaising, needed for identifying new ideas and opportunities, and then switching toward engineering, critical to the execution and exploitation of ideas (Carter & DeChurch, 2012; Gupta, Smith, & Shalley, 2006). A second approach draws upon Friedrich et al. (2009) who posit that “as different problems emerge, different skills and expertise will be more appropriate (p. 935).” The preceding approaches emphasize the dynamicism of either roles or people, but a more complex view would concurrently capture changes in both. Both of these approaches imply a certain level of churn in the leadership network. To test this implication we would need longitudinal leadership network data from each of the collectives. We begin by using p/ERGM or stochastic
actor-oriented models to estimate the temporal structural signature of transitivity (described above) for the set of longitudinal
networks for each collective. A large, positive and statistically significant value would indicate a higher level of churn caused by
transitivity than would be expected by chance. As described in the two cases above, we can use these estimates as explanatory
variables to test their influence on team performance, the outcome variable.
We began this section by acknowledging that network metrics computed using the LijRT framework offer a more nuanced
characterization of the three dimensions of collective leadership. However, being descriptive in nature, they are by themselves unable
to help us statistically test the extent towhichmember concentration, rolemultiplexity and temporal stability observed in a network
aremore thanwemight expect by chance. The problemis further exacerbated by the fact that standard statistical tests which rely on
assumptions of independence among observations are not appropriate when analyzing network data. We proposed that the three
dimensions of collective leadership would manifest themselves as distinct structural signatures in leadership networks. We offered
k-star as a structural signature that is positively associated with member concentration, multiplexity as a structural signature
positively associated with its namesake, role multiplexity, and transitivity as a temporal structural signature negatively associated
with temporal stability. We proposed the use of p*/ERGM approach to estimate parameters that index the extent to which these
structural signatures are more (or less) prevalent than by random chance. The parameter estimates can then be used as explanatory
variables to test the extent to which these structural signatures—and the dimensions of collective leadership they manifest—will
influence outcome variables such as performance or creativity.

  1. Discussion
    The fundamental nature of organizations is rapidly transforming.Work is being organized around teams, knowledge is distributed
    up and down organizational hierarchies as workers become increasingly specialized, and globalization and digitization both require
    and enable greater connectivity between distributed sets of knowledge workers. These changes have important implications for

leadership. In this review, we cumulate thinking in a relatively new genre of leadership research, one particularly well suited to
understanding the informal and emergent nature of leadership inmodern organizations.We drawout three core aspects of collective
leadership and elaborate an analytic framework enabling these aspects of collective leadership to be adequately tested. This
framework was developed to be levels-generic, so that collective leadership can be studied in a variety of collectives ranging from
teams to units to multiteam systems to full-scale organizations and the alliances between them.
We lay out an analytic framework intended to enable these core ideas about people, roles, and time to be fully tested. Extant
work on collective leadership falls within one of three categories: (1) conceptual developments, (2) empirical tests of leadership
forms on outcomes (e.g., Carson et al., 2007; Mehra et al., 2006), or (3) empirical tests of the effects of leadership roles on
outcomes (e.g., Hiller et al., 2006). The proposed framework is intended to accelerate and provide greater conceptual coherence to
empirical tests of collective leadership theory in a manner that more fully captures the essence of the phenomenon. In particular,
we hope that future research will populate two new categories: (4) empirical examinations of the factors that give rise to
particular forms of leadership, to multiplex leadership relationships, and to the likelihood that collectives can reconfigure their
leadership structures, and (5) empirical examinations of the attitudinal, cognitive, motivational, behavioral, and performance
consequences of various leadership forms, multiplex leadership relationships, and dynamic leadership structures.
5.1. Future research directions
When testing collective leadership theory, it is important to isolate the effects of collective leadership, that is people, roles, and
time, from the consequences of that leadership. For example, extensively evidence supports the role of team processes (c.f., LePine,
Piccolo, Jackson,Mathieu, & Saul, 2008) as important drivers of collective success. The true test of collective leadership is do they give
rise to these processes, in turn affecting performance? In order to be uniquely valuable, collective leadership needs to demonstrate
that there is something special in the topology of influence relationships that extends our capacity to predict collective outcomes
beyond that which we can already explain with the amount of various leader behaviors and the amount of team processes.
While much research has looked at social networks and leadership (c.f., Balkundi et al., 2011), an important point of departure
of this work is that we are explicitly looking at leadership and influence as a social network. Prior research has looked at
communication networks and drawn inferences about the effectiveness of leaders based on their embedded positions within
those communication networks (Sparrowe & Liden, 1997; Sparrowe et al., 2001). Studies of leader embeddedness in advice,
communication, friendship or other types of networks essentially study situational moderators of the effects of leadership. Others
have focused directly on the leadership relations rather than the communication ties. Both types of investigations of networks are
useful, but they yield different inferences about leadership. Investigations of leadership and influence networks (e.g., Siebert,
Sparrowe, & Liden, 2003) are necessary to directly test propositions about collective leadership.
Leadership ties can be weak or strong. In network terms, this implies that the leadership times are valued or continuous and
not binary (influence relationship either exists or not). Unfortunately contemporary versions of the p*/ERGM analytic techniques
require that the focal relationship (in our case, one actor’s perception of another actor’s leadership role) is constrained to be
binary. While this is an area of active research, this is certainly an analytic limitation of the proposed framework at the current
time.
5.2. Conclusion
Modern leadership theory is inherently relational, holding that leadership is the confluence of leaders, followers, and their
relationships (e.g., Avolio, Walumbwa, & Weber, 2009; Graen & Uhl-Bien, 1995). Such a relational perspective is well suited to
testing with network approaches, particularly when one considers the implications of topology in various collectives. Network
methods provide an appropriate language to distinguish between different topologies of collective leadership that involve
multiple people, exhibiting multiple types of influence relationships, with relational patterns that are fluid over the course of
team development. Further, network methods provide a higher resolution multi-level approach to study the emergence of these
different forms of leadership based on attributes of individuals (leaders and members), dyadic relational ties (such as trust), as
well as higher-order triadic (balance) and group level effects (such as cohesion). The precision afforded by network methods will
help to more accurately reflect the processes posited by extant leadership theories.
We have summarized the core thinking about collective leadership over the past decade, and distilled out three integral ideas
about collective leadership that then translate into an operationalization framework so that ideas can be tested appropriately
with network analysis. The fact that empirical work in this area has attended to one of these defining aspects, i.e., either people
(e.g., Carson et al., 2007), roles (e.g., Hiller et al., 2006) or time (e.g., Erez et al., 2002) but not multiple aspects, evidences the need
for such a framework. Our primary contribution is to enable better translation between the conceptual advances of understanding
leadership as complex and emergent with corresponding advances in network analytic methodology.
In closing, we hope this framework advances research on collective leadership in two ways. First, the framework serves to
guide research practices, ensuring that researchers make informed decisions in choosing the appropriate network elicitation and
structural representation techniques most suitable to answering their conceptual questions. The second advancement is that such
a framework may actually broaden the theoretical approaches. The relational paradigm of network analytic methods may well
generate new types of questions on the emergence, patterns, and effects of leadership at multiple levels of analysis (Monge &
Contractor, 2003). Thus, we hope that a richer understanding of the range of elicitation and representational techniques available

in network approaches will enable leadership researchers to generate new questions, and new types of questions about collective
leadership.
Acknowledgment
This material is based upon work supported by the National Science Foundation under Grant Nos. OCI-1056217, IIS-0838564 &
SBE-1063901 as well as the Army Research Laboratory under Cooperative Agreement Number W911NF-09-2-0053.
References
Albrecht, T. L., & Hall, B. J. (1991). Facilitating talk about new ideas: The role of personal relationships in organizational innovation. Communication Monographs,
58, 273–288.
Albrecht, T. L., & Ropp, V. A. (1984). Communicating about innovation in networks of three U.S. organizations. Journal of Communication, 34, 78–91.
Anderson, C. J., Wasserman, S., & Crouch, B. (1999). A p* primer: Logit models for social networks. Social Networks, 21, 37–66.
Avolio, B. J., Jung, D. I., & Sivasubramaniam, N. (1996). Building highly developed teams: Focusing on shared leadership processes, efficacy, trust, and performance.
In M. M. Beyerlein, & D. A. Johnson (Eds.), Advances in interdisciplinary study of work teams: Team leadership (pp. 173–209). Greenwich, CT: JAI Press.
Avolio, B. J., Walumbwa, F. O., & Weber, T. J. (2009). Leadership: Current theories, research, and future directions. Annual Review of Psychology, 60, 421–449.
Bales, R. (1950). Interaction process analysis: A method for the study of small groups. Cambridge, MA: Addison-Wesley.
Bales, R. F. (1958). Task roles and social roles in problem-solving groups. Readings in social psychology. New York: Holt, Reinhard, & Winston.
Bales, R., & Slater, P. (1955). Role differentiation in small decision-making groups. In T. Parsons, & R. Bales (Eds.), Family, socialization and interaction process
(pp. 259–306). Glencoe: The Free Press.
Balkundi, P., Kilduff, M., & Harrison, D. A. (2011). Centrality and charisma: Comparing how leader networks and attributions affect team performance. Journal of
Applied Psychology, 96, 1209–1222.
Barabasi, A. L., & Albert, R. (1999). Emergence of scaling in random networks. Science, 286, 509–512.
Barry, D. (1991). Managing the bossless team: Lessons in distributed leadership. Organizational Dynamics, 20, 31–47.
Bass, B. M. (1998). Transformational leadership: Individual, military, and educational impact. Mahwah, NJ: Erlbaum.
Brass, D. J. (1985). Men’s and women’s networks: A study of interaction patterns and influence in an organization. Academy of Management Journal, 28, 327–343.
Brass, D., & Krackhardt, D. (1999). The social capital of twenty-first century leaders. In J. G. Hunt, & R. L. Phillips (Eds.), Out-of-the-box leadership challenges for the
21st century army (pp. 179–194). Amsterdam: Elsevier B.V.
Burns, J. M. (1978). Leadership. New York: Harper & Row.
Burt, R. S. (1987). Social contagion and innovation: Cohesion versus structural equivalence. The American Journal of Sociology, 92, 1287–1335.
Carson, J. B., & Tesluk, P. E. (2007). Leadership from within: A look at leadership roles in teams. Paper presented at the 67th Annual Meeting of the Academy of
Management, Philadelphia.
Carson, J. B., Tesluk, P. E., & Marrone, J. A. (2007). Shared leadership in teams: An investigation of antecedent conditions and performance. Academy of Management
Journal, 50, 1217–1234.
Carte, T., Chidambaram, L., & Becker, A. (2006). Emergent leadership in self-managed teams: A longitudinal study of concentrated and shared leadership
behaviors. Group Decision and Negotiation, 15, 323–343.
Carter, D. R., DeChurch, L. A., & Zaccaro, S. J. (August, 2012). Emergent leadership network structures in global virtual teams: Impact on innovation. In E.
Campbell-Bush & K. Bartol (Co-Chairs), Advances in highly virtual teams: Key composition, leadership, and shared process components. Symposium at the
Academy of Management annual meeting, Boston, MA.
Contractor, N., Wasserman, S., & Faust, K. (2006). Testing multi-theoretical multilevel hypotheses about organizational networks: An analytic framework and
empirical example. Academy of Management Review, 31, 681–703.
Cox, J. F., Pearce, C. L., & Perry, M. L. (2003). Toward a model of shared leadership and distributed influence in the innovation process: How shared leadership can
enhance new product development. In C. L. Pearce, & J. A. Conger (Eds.), Shared leadership: Reframing the hows and whys of leadership. Thousand Oaks, CA:
Sage Publications.
Cross, R., Borgatti, S. P., & Parker, A. (2001). Beyond answers: Dimensions of the advice network. Social Networks, 23, 215–235.
Denis, J. L., Langley, A., & Sergi, V. (2012). Leadership in the plural. The Academy of Management Annals, 6, 211–283.
Ensley, M. D., Hmieleski, K. M., & Pearce, C. L. (2006). The importance of vertical and shared leadership within new venture top management teams: Implications
for the performance of startups. The Leadership Quarterly, 17, 217–231.
Erez, A., LePine, J. A., & Elms, H. (2002). Effects of rotated leadership and peer evaluation on the functioning and effectiveness of self-managed teams: A quasi-experiment.
Personnel Psychology, 55, 929–948.
Faust, K. (1988). Comparison of methods for positional analysis: Structural and general equivalences. Social Networks, 10, 313–341.
Fletcher, J. K., & Käufer, K. (2003). Shared leadership: Paradox and possibility. In C. L. Pearce, & J. A. Conger (Eds.), Shared leadership: Reframing the hows and whys
of leadership (pp. 21–46). Thousand Oaks, CA: Sage.
Frank, O. (1981). A survey of statistical methods for graph analysis. In S. Leinhardt (Ed.), Sociological methodology (pp. 110–155). San Francisco: Jossey-Bass.
Frank, O., & Strauss, D. (1986). Markov graphs. Journal of the American Statistical Association, 81, 832–842.
Freeman, L. (1977). A set of measures of centrality based upon betweenness. Sociometry, 40, 35–41.
Friedrich, T. L., Vessey, W. B., Schuelke, M. J., Ruark, G. A., & Mumford, M. D. (2009). A framework for understanding collective leadership: The selective utilization
of leader and team expertise within networks. The Leadership Quarterly, 20, 933–958.
Gersick, C. J. G. (1989). Marking time: Predictable transitions in task groups. Academy of Management Journal, 32, 274–309.
Gibb, C. A. (1954). Leadership. In G. Lindzey (Ed.), Handbook of social psychology, 2. (pp. 877–917)Reading, MA: Addison-Wesley.
Gibbs, J. P., & Martin, W. T. (1962). Urbanization, technology and the division of labor. American Sociological Review, 27, 667–677.
Graen, G. B., & Uhl-Bien, M. (1995). Relationship-based approach to leadership: Development of leader–member exchange (LMX) theory of leadership over 25
years: Applying a multi-level multi-domain perspective. The Leadership Quarterly, 6, 219–247.
Gronn, P. (2002). Distributed leadership as a unit of analysis. The Leadership Quarterly, 13, 423–451.
Gupta, A. K., Smith, K. G., & Shalley, C. (2006). The interplay between exploration and exploitation. Academy of Management Journal, 49, 693–706.
Hackman, J. R., & Walton, R. E. (1986). Leading groups in organizations. In P. S. Goodman (Ed.), Designing effective work groups. San Francisco: Jossey-Bass.
Hanneman, R. A., & Riddle, M. (2005). Introduction to social network methods. Riverside, CA: University of California, Riverside (published in digital form at: http://
faculty.ucr.edu/hanneman/)
Hiller, N. J., Day, D. V., & Vance, R. J. (2006). Collective enactment of leadership roles and team effectiveness: A field study. The Leadership Quarterly, 17, 387–397.
Holland, P. W., & Leinhardt, S. (1971). Transitivity in structural models of small groups. Comparative Group Studies, 2, 107–124.
Hollander, E. P. (1961). Emergent leadership and social influence. In L. Petrullo, & B. M. Bass (Eds.), Leadership and interpersonal behavior (pp. 30–47). New York:
Holt, Rinehart, and Winston.
Hollander, E. P. (1985). Leadership and power. In G. Lindzey, & E. Aronson (Eds.), Handbook of social psychology (pp. 485–538). (3rd ed.). New York: Random
House.
Homans, G. C. (1961). Social behaviour: Its elementary forms. New York: Harcourt, Brace & World, Inc.

Hoppe, B., & Reinelt, C. (2010). Social network analysis and the evaluation of leadership networks. The Leadership Quarterly, 21, 600–619.
Kaiser, R. B., Hogan, R., & Craig, S. B. (2008). Leadership and the fate of organizations. American Psychologist, 63, 96–110.
Katz, D., & Kahn, R. L. (1978). The social psychology of organizations (2nd ed.). New York: Wiley.
Kellett, J. B., Humphrey, R. H., & Sleeth, R. G. (2002). Empathy and complex task performance: Two routes to leadership. The Leadership Quarterly, 13, 523–544.
Klein, K. J., Ziegert, J. C., Knight, A. P., & Xiao, Y. (2006). Dynamic delegation: Shared, hierarchical, and deindividualized leadership in extreme action teams.
Administrative Science Quarterly, 51, 590–621.
LePine, J. A., Piccolo, R. F., Jackson, C. L., Mathieu, J. E., & Saul, J. R. (2008). A meta-analysis of teamwork processes: Tests of a multidimensional model and
relationships with team effectiveness criteria. Personnel Psychology, 61, 273–307.
Lincoln, J. R., & Miller, J. (1978). Work and friendship ties in organizations: A comparative analysis of relational networks. Administrative Science Quarterly, 24,
181–199.
Marks, M. A., Mathieu, J. E., & Zaccaro, S. J. (2001). A temporally based framework and taxonomy of team processes. Academy of Management Review, 26, 356–376.
Mayo, M. C., Meindl, J. R., & Pastor, J. C. (2003). Shared leadership in work teams: A social network approach. In C. Perce, & J. Conger (Eds.), Shared leadership:
Reframing the hows and whys of leadership (pp. 193–214). Thousand Oaks, CA: Sage.
Mehra, A., Smith, B. R., Dixon, A. L., & Robertson, D. (2006). Distributed leadership in teams: The network of leadership perceptions and team performance. The
Leadership Quarterly, 17, 232–245.
Mohammed, S., Klimoski, R., & Rentsch, J. R. (2000). The measurement of team mental models: We have no shared schema. Organizational Research Methods, 3,
123–165.
Monge, P. R., & Contractor, N. S. (2003). Theories of communication networks. New York: Oxford University Press.
Pattison, P. E., & Wasserman, S. (1999). Logit models and logistic regressions for social networks. II. Multivariate relations. British Journal of Mathematical and
Statistical Psychology, 52, 169–194.
Pearce, C. L. (1997). The determinants of change management team (CMT) effectiveness: A longitudinal investigation. Unpublished doctoral dissertation,
University of Maryland, College Park.
Pearce, C. L., & Conger, J. A. (Eds.). (2003). Shared leadership: Reframing the hows and whys of leadership. Thousand Oaks, CA: Sage Publications.
Pearce, C. L., & Sims, H. P. (2002). The relative influence of vertical vs. shared leadership on the longitudinal effectiveness of change management teams. Group
Dynamics: Theory, Research, and Practice, 6, 172–197.
Robins, G., Pattison, P., Kalish, Y., & Lusher, D. (2007a). An introduction to exponential random graph (p) models for social networks. Social Networks, 29, 173–191. Robins, G. L., Pattison, P. E., & Wasserman, S. (1999). Logit models and logistic regressions for social networks: III. Valued relations. Psychometrika, 64, 371–394. Robins, G., Snijders, T., Wang, P., Handcock, M., & Pattison, P. (2007b). Recent developments in exponential random graph (p) models for social networks. Social
Networks, 29, 192–215.
Seers, A., Keller, T., & Wilkinson, J. M. (2003). Can team members share leadership? Foundations in research and theory. In C. L. Pearce, & J. A. Conger (Eds.), Shared
leadership: Reframing the hows and whys of leadership. Thousand Oaks, CA: Sage Publications.
Shannon, C. E. (1948). A mathematical theory of communication. The Bell System Technical Journal, 27, 379–423.
Shumate, M., & Palazzolo, E. (2010). Exponential random graph (p) models as a method for social network analysis in communication research. Communication Methods and Measures, 4, 341–371. Siebert, S. E., Sparrowe, R., & Liden, R. (2003). A group exchange structure approach to leadership in groups. In C. L. Pearce, & J. A. Conger (Eds.), Shared leadership: Reframing the hows and whys of leadership. Thousand Oaks, CA: Sage Publications. Sparrowe, R. T., & Liden, R. C. (1997). Process and structure in leader–member exchange. The Academy of Management Review, 22, 522–552. Sparrowe, R. T., Liden, R. C., Wayne, S. J., & Kraimer, M. L. (2001). Social networks and the performance of individuals and groups. Academy of Management, 2, 316–325. Steglich, C., Snijders, T. A. B., & Pearson, M. (2010). Dynamic networks and behavior: Separating selection from influence. Sociological Methodology, 40, 329–393. Taggar, S., Hackett, R., & Saha, S. (1999). Leadership emergence in autonomous work teams: Antecedents and outcomes. Personnel Psychology, 52, 899–926. Tuckman, B. W. (1965). Developmental sequence in small groups. Psychological Bulletin, 63, 384–399. Wang, P., Robins, G., & Pattison, P. (2006). LPNet: A program for the simulation and estimation of longitudinal exponential random graph models. University of Melbourne. Wasserman, S., & Faust, K. (1994). Social network analysis: Methods and applications. Cambridge: Cambridge University Press. Wasserman, S., & Pattison, P. E. (1996). Logit models and logistic regressions for social networks: I. An introduction to Markov graphs and p. Psychometrika, 61,
401–425.
Wasserman, S., & Robins, G. L. (2005). An introduction to random graphs, dependence graphs, and p*. In P. Carrington, J. Scott, & S. Wasserman (Eds.), Models and
methods in social network analysis (pp. 148–161). New York: Cambridge University Press.
Zaccaro, S. J., & Marks, M. A. (1999). The roles of leaders in high performance teams. In E. Sundstrom, & Associates (Eds.), Supporting work team effectiveness
(pp. 95–125). San Francisco: Jossey-Bass.
Zhu, H., Kraut, R. E., & Kittur, A. (2012) Organizing without formal organization: Group identification, goal setting and social modeling in directing online
production. In Proceedings of the 2012 ACM conference on Computer-Supported Cooperative Work (CSCW ’12).
Zigurs, I., & Kozar, K. (1994). An exploratory study of roles in computer-supported groups. MIS Quarterly, 4, 277–297.