An Information Flow Model for Conflict and Fission in Small Groups

Abstract

Abstract. The paper is devoted to game-theoretic methods for community detection in networks. The traditional methods for detecting community structure are based on selecting denser subgraphs inside the network. Here we propose to use the methods of cooperative game theory that highlight not only the link density but also the mechanisms of cluster formation. Specifically, we suggest two approaches from cooperative game theory: the first approach is based on the Myerson value, whereas the second approach is based on hedonic games. Both approaches allow to detect clusters with various resolution. However, the tuning of the resolution parameter in the hedonic games approach is particularly intuitive. Furthermore, the modularity based approach and its generalizations can be viewed as particular cases of the hedonic games.

The Cohesiveness of Blocks In Social Networks: Node Connectivity and Conditional Density

“…Zachary (1975Zachary ( , 1977 argued that when conflicts between rival leaders within a group are sufficiently intense, the group would segment through dissolution of the minimum number of links needed to separate into two. Anticipating our analysis of this case in Section IV, we take issue with this adhesionbased hypothesis for several reasons.…”

“…When the edges of graphs are weighted, or we convert a weighted graph to an equivalent multigraph, we can make use of Ford and Fulkerson's (1956) It is this theorem that Zachary (1975Zachary ( , 1977 uses to partition his karate club network, whose leaders are in conflict, into two halves: those who are most adhesively connected (by the greatest number of edge-independent paths ϭ the least-edge cutset) with the club's administrator and those most adhesively connected to the club's karate instructor. We discussed this case in Section I.C, in which our critique of Zachary's adhesion-based minimum 30 Dirac (1960) showed that this result, in which each edge e has a numerical weight w~e!, is a straightforward corollary of Menger's Theorem B.…”

“…AN EMPIRICAL EXAMPLE: ZACHARY'S KARATE CLUB Zachary's (1975Zachary's ( , 1977 two-year ethnographic network study of 34 members of a karate club is a good proving ground to examine concepts, measures and hypotheses involving relational aspects of social solidarity. This section provides an illustration of how measures of cohesion are used to predict the outcome variable of sides taken in a factional dispute from the boundaries of nested cohesive sets.…”

Checking the reliability of a linear-programming based approach towards detecting community structures in networks

“…We demonstrated that this strategy yields indeed pretty good solutions for some well known benchmark problems including Zachary's Karate Club [39] and the Chesapeake-Bay Food Web compiled by Baird and Ulanowicz [3]: For Zachary's Karate club, our method produced exactly the "historically correct" partition.…”

Orca Reduction and ContrAction Graph Clustering

“…Figure 3 shows Orca's results, a clear success. The second example was compiled by Wayne Zachary [32] while doing a study on the social structure of friendship between the members of a university sports club. The two real-world factions are indicated by color in Figure 4.…”