Prominence

Centrality and Prestige Measurements

Prominence is frequently attributed to actors who have many ties in the network because such a position is associated with high visibility and ability to influence a large number of people. An actor's degree centrality (or degree) is simply the number of ties the actor has to others in the network. Thus, in a network of mutual friendship, a person with many friends will have high degree centrality.

A more sophisticated alternative begins with the degree measure of prominence and then weights each actor's prominence by the prominence of each of its peers, which is in turn weighted by the prominence of each of those peers, and so on. This recursive measure represents an actor's connectedness to highly connected peers and takes all direct and indirect network paths from the focal actor into account. Network analysis software computes this measure directly by finding the first eigenvector of the matrix representing ties among individuals and is often called eigenvector centrality.

Two other measures are based on the set of geodesics, or the shortest paths connecting any two distinct Actors I and J (where paths may be indirect, through other actors in the network). For example, closeness centrality is constructed by summing the geodesic path lengths between a focal Actor I and each other member reachable from I through the network. (Typically, the inverse of this total is used for the final measure, to ensure that all centrality scores lie between zero and one and that the most central actors receive the highest scores). Closeness centrality, therefore, captures the shortness of the network paths connecting an actor to all others and may be interpreted as the ease and efficiency by which an actor can access information and other resources through the network.

An actor may also be prominent by being on paths that bridge different parts of the network, because many others may rely on the actor for relaying instructions or other information. Betweenness centrality is computed from the set of geodesics by finding the proportion of [Page 721]the shortest paths among all other actors that contain the focal actor.

In a directed network, a tie is not a symmetric connection between two actors but an asymmetric link, going from one actor to another. The simplest measure of prominence for directed networks simply breaks down the degree count for incoming ties (in-degree) and outgoing ties (out-degree). Either the in-degree or out-degree measure may be interpreted as prominence, depending on the meaning of the individual tie. For example, if a tie represents a supervisory relation, then an actor with a high out-degree is especially prestigious. If a tie represents seeking advice or support, then an actor with a high in-degree is especially prestigious.

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