Leadership Networks

Social network analysis (SNA) is a set of theories, tools, and processes for better understanding the relationships and structure of a network.

In social networks, "nodes" of the network are people and the "links" are the relationships between people. Sometimes nodes are also used to represent events, ideas, objects, or other things. SNA practitioners collect network data, analyze the data (e.g., with special-purpose SNA software), and often produce maps or pictures that display the patterns of connections between the nodes of the network. These maps reveal characteristics of the network that help guide participants as they evaluate their network and plan ways to improve their collective ability to identify and achieve shared goals. (The maps in this paper were created using SNA computer programs by Borgatti (2002) and Brandes and Wagner (2004)).

Basic Network Concepts

Many mathematical techniques are available to measure networks (Wasserman and Faust, 1994); here we highlight a few that are especially useful for those who participate in, run, and fund leadership networks. Later in the paper we demonstrate how to use these metrics to understand and evaluate specific leadership networks.

Bonding and bridging

Bonding and bridging are two different kinds of connectivity that we distinguish. Bonding denotes connections in a tightly knit group. Bridging denotes connections to diverse others. See Figure 1 for an illustration. These terms are commonly used in the social capital literature (Putnam, 2001). In the SNA literature, bonding and bridging are often called "closure" and "brokerage" (Burt, 2005); also, "strong ties" and "weak ties" are important related SNA concepts that we incorporate into our bonding-bridging usage (Granovetter, 1983). Analyzing network data to measure bonding and bridging helps to predict important outcomes such as efficiency and innovation: bonding indicates a sense of trusted community where interactions are familiar and efficient; bridging indicates access to new resources and opportunity for innovation and profit (Burt, 2005).

Clusters

A cluster in a network is a tightly knit subgroup where bonding is occurring. Finding clusters is one of the most important leadership network applications of SNA, specifically used to illuminate important subgroups that were previously unrecognized. Clusters can be displayed visually with a network map, as shown by the three highlighted clusters in Figure 1. Algorithms that find clusters work by measuring local variations in density and links per node, two fundamental network metrics described below.

Core and Periphery

Many networks feature a core/periphery structure. The core is a dominant central cluster, while the periphery has relatively few connections (Borgatti and Everett, 1999).

Density and Links per Node

Density is the number of links that exist in a network divided by the maximum possible number of links that could exist in the network. Figure 2 shows an example of this calculation:

Roughly speaking, density can be used to define clusters as follows: a cluster is a local region in a network with relatively high density and relatively few links to other clusters. Formal mathematical definitions of clusters and algorithms for finding clusters are surveyed by Brandes and Erlebach (2005).

Links per node is the total number of links divided by the total number of nodes in the network. Continuing with the example from Figure 2, a network with a total of 6 links joining 5 nodes has 1.2 links per node. Density and links per node both have strengths and weaknesses when used to assess leadership networks. In general, we recommend links per node as a more intuitive metric for leadership networks: It is much less prone to misinterpretation than density. We say more about this in the "Issues and Risks" section of this paper.

Bridgers and Betweenness Centrality

Bridgers are individuals in a network who have connections to different clusters. Finding bridgers is the flip side of finding clusters, and bridgers can be highlighted visually just as clusters can; there is one notable bridger in Figure 1. Bridgers in a leadership network provide valuable opportunities for innovation, growth, and impact; yet bridgers are easy to overlook. Finding bridgers is an important application of SNA in leadership networks.

Finding bridgers in a network is typically done with the calculation called betweenness centrality (Freeman, 1979). This calculation indicates how often one individual is likely to be an important relay point between other network members. Another metric used to find bridgers is network constraint (Burt, 2004, 2005). An individual's network constraint measures the extent to which he links to others that are already linked to each other. Low network constraint means that an individual has links to others who are not already linked to each other. High betweenness centrality and low network constraint both indicate bridging.

Hubs and Indegree Centrality

Hubs are individuals in a network with the most influence. Whether hubs bridge across clusters or bond within a cluster (or some combination), they are highly sought-after by other network members.

Finding hubs of influence in a network usually starts with tracking directed links as opposed to undirected links. Figure 3 illustrates the distinction:

Given a network of directed relationships (e.g., "knows of," "seeks advice from"), indegree centrality (or just "indegree") counts how many relationships point towards an individual; this provides a simple measure of influence (Freeman, 1979).

More advanced influence metrics build on indegree and consider not just how many others seek the advice of a particular person, but also how influential those other advice-seekers are. A person whose advice is sought by someone who is highly influential may have a higher influence score than one whose advice is sought by many non-influencers. Bonacich and Lloyd (2001) overview several advanced influence metrics and explain how most of them compute nearly the same thing. In most cases, we recommend using indegree, because it communicates the basic point without unnecessary complications.

Structural Equivalence

Amazon.com made structural equivalence famous as the calculation behind its recommendations: "People who bought books A and B also bought books C and D." This Amazon.com example considers both people and books as members of a single network. Links in this network join people to the books they have purchased. People who buy mostly the same books have high structural equivalence; people who buy mostly different books have low structural equivalence.

Structural equivalence in leadership networks is based not on shared reading lists but rather on shared activities, goals, or interests. For example, Figure 4 displays members of a leadership network as circles and their professional activities as squares. Links indicate which people engage in which activities. The larger squares denote the more common activities. The layout of the map places people next to those who share the same activities, and it also places activities next to other activities that share the same participants (Borgatti, 2002; Gower, 1971; Hanneman and Riddle, 2005). There is a group of 13 people who engage in exactly the same set of activities; they are highlighted near the bottom left. The nodes in this group all have high structural equivalence with each other. Similarly, the three activities in the middle, "expand networks," "design programs," and "implement programs," share many of the same participants; these three nodes have relatively high structural equivalence with each other.

Structural equivalence is an important metric for leadership networks. It is similar to finding clusters, in that both techniques illuminate important subgroups that were previously unrecognized. Unlike finding clusters, however, structural equivalence can work without any information about who knows whom; it is rather like Amazon.com offering to introduce people who bought the same books. For those seeking to bond or to bridge, this information is extremely useful.

Asking network members to report what relationships they have with all other network members can raise difficult challenges, which are discussed in the "Issues and Risks of SNA" section of this paper. By comparison, it is easier to collect data about which network members associate themselves with which activities, or what goals each person considers important as a member of the network. Because structural equivalence can make use of data that is easily collected, and other SNA techniques require data that is harder to obtain, it is especially valuable to have structural equivalence as a metric in one's SNA toolbox.

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