Group Structure and the Behavior of Individuals in Small Groups

Centrality in social networks conceptual clarification

“…Thus, p3 is an example of a point of maximum degree in a five-point graph. Shaw ( 1954) introduced the idea of using degree as an index of point centrality, and along with other writers (Faucheux and Moscovici 1960; Mackenzie 1964Mackenzie , 1966aCzepiel 1974;Nieminen 1973Nieminen , 1974Rogers 1974) who conceived of point centrality in this way, he apparently found it so intuitively appealing that he did not bother to discuss or elaborate its conceptual foundations at all. For these writers, centrality means degree.…”

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

“…The second intuition grows out of the idea that people are somehow central to the degree they stand between others on the paths of communication (Bavelas 1948;Shimbel 1953;Shaw 1954;Cohn and Marriott 1958;Anthonisse 1971;Freeman 1977;Friedkin 1991). Such people can facilitate or inhibit the communication of others and are, therefore, in a position to mediate the access of others to information, power, prestige or influence.…”

“…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).…”

The Power of Quasi-Shortest Paths: $\rho$ -Geodesic Betweenness Centrality

“…The idea behind the betweenness centrality is that the more a node υ k is centrally positioned, the more it falls on shortest paths between other nodes [22], [23], [24], [25]. Hence, such nodes are strategically positioned and can influence the network by controlling the flow of information.…”