On the centrality in a graph

Abstract

Abstract.— The paper considers the concept of centrality in an undirected graph. A system of axioms and an index for centrality satisfying the axioms are presented. The index is based on the degrees of the vertices in a given undirected graph, and it will enlarge the class of comparable graphs with respect to a centrality measure.

Environmental context, managerial cognition, and strategic action: an integrated view

“…Degree centrality is computed as (Borgatti, 2005;Freeman, 1978Freeman, /1979Scott, 2000): The closeness centrality is obtained by using the shortest paths from the focal concept to reach all other concepts in the network as follows (Freeman, 1978(Freeman, /1979Nieminen, 1974): where: C D (P k ) = number of concepts connected to concept k d(p i , p k ) = distances: shortest number of paths that concept p i has to go through to reach each concept in the network n = number of concepts in the causal map Appendix IV illustrates the degree and closeness centrality measures for a causal map comprising four concepts (A, B, C, and D). Concept C is the most central concept in the network based on degree (1.0) as well as closeness (1.0) centrality because it is most connected and has the shortest distance to other concepts in the network.…”

Centrality in valued graphs: A measure of betweenness based on network flow

“…First there are those who view a person as central in a social network to the extent that he or she is somehow close to everyone else in the network (Bavelas 1950;Katz 1953;Shaw 1954;Harary 1959;Faucheux and Moscovici 1960;Garrison 1960;Beauchamp 1965;Pitts 1965;Hubbell 1965;Mackenzie 1966;Sabidussi 1966;Bonacich 1972Bonacich , 1987Coleman 1973;Nieminen 1973Nieminen , 1974Moxley and Moxley 1974;Rogers 1974;Czepiel 1974;Kajitani and Maruyama 1976;Burt 1982;Mizruchi, Mariolis, Schwartz and Mintz 1986;Stephenson and Zelen 1989;Friedkin 1991).…”

Can System Dynamics Learn from Social Network Analysis?

“…Degree centrality of a vertex in a network is simply the number of edges connected to it (Nieminen, 1974;Newman, 2010, p.133). In a directed network of n vertices, however, the degree of vertex i, , can be further sub-divided into in-degree and out-degree .…”