# Nm3/Fragment 1041 16

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Seite: 1041, Zeilen: 16-33
Quelle: Balasundaram et al 2006
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Modeling a cohesive subgroup mathematically has long been a subject of interest in social network analysis. One of the earliest graph models used for studying cohesive subgroups was the clique model (Luce, R., Perry A., 1949). A clique is a subgraph in which there is an edge between any two vertices. However, the clique approach has been criticized for its overly restrictive nature (Scott, J, 2000), Wasserman, S., Faust, K., 1994) and modeling disadvantages (Siedman [sic], S. B., Freeman, L. C., 1992).

Alternative approaches were suggested that essentially relaxed the definition of cliques. Clique models idealize three important structural properties that are expected of a cohesive subgroup, namely, familiarity (each vertex has many neighbors and only a few strangers in the group), reachability (a low diameter, facilitating fast communication between the group members) and robustness (high connectivity, making it difficult to destroy the group by removing members).

Different models relax different aspects of a cohesive subgroup. Luce R. introduced a distance based model called n-clique (Luce, R., 1950). This model was also studied along with a variant called n-clan by Mokken (Mokken, R., 1979).

However, their originally proposed definitions required some modifications to be more meaningful mathematically.

Modeling a cohesive subgroup mathematically has long been a subject of interest in social network analysis. One of the earliest graph models used for studying cohesive subgroups was the clique model [35]. A clique is a subgraph in which there is an edge between any two vertices. However, the clique approach has been criticized for its overly restrictive nature [2,52] and modeling disadvantages [47,25].

Alternative approaches were suggested that essentially relaxed the definition of cliques. Clique models idealize three important structural properties that are expected of a cohesive subgroup, namely, familiarity (each vertex has many neighbors and only a few strangers in the group), reachability (a low diameter, facilitating fast communication between the group members) and robustness (high connectivity, making it difficult to destroy the group by removing members). Different models relax different aspects of a cohesive subgroup. [34] introduced a distance based model called k-clique and [2] introduced a diameter based model called k-club. These models were also studied along with a variant called k-clan by Mokken [38]. However, their originally proposed definitions required some modifications to be more meaningful mathematically.

2. Alba, R.: A graph-theoretic definition of a sociometric clique. Journal of Mathematical Sociology 3, 113–126 (1973)

25. Freeman, L.C.: The sociological concept of “group”: An empirical test of two models. American Journal of Sociology 98, 152–166 (1992)

34. Luce, R.: Connectivity and generalized cliques in sociometric group structure. Psychometrika 15, 169–190 (1950)

35. Luce, R., Perry, A.: A method of matrix analysis of group structure. Psychometrika 14, 95–116 (1949)

38. Mokken, R.: Cliques, clubs and clans. Quality and Quantity 13, 161–173 (1979)

47. Seidman, S.B., Foster, B.L.: A graph theoretic generalization of the clique concept. Journal of Mathematical Sociology 6, 139–154 (1978)

52. Wasserman, S., Faust, K.: Social Network Analysis. Cambridge University Press (1994)

 Anmerkungen The source is not given. The text has been copied verbatim and also all references to the literature are identical with the source. Sichter (Hindemith), WiseWoman