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Research using techniques from social network analysis have expanded dramatically in recent years. The availability of network data and the recognition that social network techniques can provide an additional perspective have contributed to this expansion. Social network data are not always in a standard network form and, in many instances, consists of two distinct groups with ties between groups and no within group ties. For example, people attending events or meetings, authors collaborating on research outputs, or directors on boards of companies. Such data are known as two-mode data. Recently, Everett and Borgatti suggested a general approach for analyzing two-mode data. They suggested forming two one-mode data sets, analyzing these separately, and then recombining the results using the original data. One under-explored area in their work is in how this method can be applied to centrality problems; an issue we seek to begin to address here.

In a paper examining informal networks and organizational crisis, Krackhardt and Stern (1988) proposed a measure assessing the extent to which relations in a network were internal to a group as opposed to external. They called their measure the E-I index. The measure is now in wide use and is implemented in standard network packages such as UCINET (Borgatti et al., 2002). The measure is based on a partition-based degree centrality measure and as such can be extended to other centrality measures and group level data. We explore extensions to closeness, betweenness and eigenvector centrality, and show how to apply the technique to sets of subgroups that do not form a partition. In addition, the extension to betweenness suggests a linkage to the Gould and Fernandez brokerage measures, which we explore. © 2012 Elsevier B.V.

Centrality measures are based upon the structural position an actor has within the network. Induced centrality, sometimes called vitality measures, take graph invariants as an overall measure and derive vertex level measures by deleting individual nodes or edges and examining the overall change. By taking the sum of standard centrality measures as the graph invariant we can obtain measures which examine how much centrality an individual node contributes to the centrality of the other nodes in the network, we call this exogenous centrality. We look at exogenous measures of degree, closeness and betweenness. © 2010 Elsevier B.V.