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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.

Written by a stellar team of experts, Analyzing Social Networks is a practical book on how to collect, visualize, analyze and interpret social network data with a particular emphasis on the use of the software tools UCINET and Netdraw. The book includes a clear and detailed introduction to the fundamental concepts of network analyses, including centrality, subgroups, equivalence and network structure, as well as cross-cutting chapters that helpfully show how to apply network concepts to different kinds of networks. Written using simple language and notation with few equations, this book masterfully covers the research process, including: * The initial design stage * Data collection and manipulation * Measuring key variables * . Exploration of structure * Hypothesis testing * Interpretation This is an essential resource for students, researchers and practitioners across the social sciences who want to use network analysis as part of their research.