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Autor     B. Balasundaram, S. Butenko, I. V. Hicks, S. Sachdeva
Titel    Clique Relaxations in Social Network Analysis: The Maximum k-plex Problem
Datum    27. January 2006
Anmerkung    This is a preprint: date according to PDF file properties, confirmed by: [1], The Memon & Larsen paper was presented in August 2006: [2]
URL    http://www.caam.rice.edu/~ivhicks/kplex.general.pdf
Webcite    http://www.webcitation.org/6MzMGGm2A

Literaturverz.   

no
Fußnoten    no
Fragmente    4


Fragmente der Quelle:
[1.] Nm3/Fragment 1037 35 - Diskussion
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Cohesion analysis (also called structural cohesion) is often used to explain and develop sociological theories. Members of a cohesive subgroup tend to share information, have homogeneity of thought, identity, beliefs, behavior, even food habits and illnesses (Wasserman, S., Faust, K, 1994). Cohesion analysis is also believed to influence emergence of consensus among group members.

25. Wasserman, S., Faust, K.: Social Network Analysis. Cambridge University Press.1994.

Social cohesion is often used to explain and develop sociological theories. Members of a cohesive subgroup tend to share information, have homogeneity of thought, identity, beliefs, behavior, even food habits and illnesses [52]. Social cohesion is also believed to influence emergence of consensus among group members.

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

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[Examples of cohesive sub-] groups include religious cults, terrorist cells, criminal gangs, military platoons, tribal groups and work groups etc.

[...]

Some direct application areas of social networks include studying terrorist networks (Sageman, M., 2004, Berry, N. et al., 2004), which is essentially an [sic] special application of criminal network analysis that is intended to study organized crimes such as terrorism, drug trafficking and money laundering (McAndrew, D., 1999, Davis, R. H., 1981). Concepts of social network analysis provide suitable data mining tools for this purpose (Chen, H., et al., 2004).

Figure 1 shows an example of a terrorist network, which maps the links between terrorists involved in the tragic events of September 11, 2001. This graph was constructed by Valdis Krebs (Krebs, V., 2002) using the public data that were available before, but collected after the event. Even though the information mapped in this network is by no means complete, its analysis may still provide valuable insights into the structure of a terrorist organization.

Examples of cohesive subgroups include religious cults, terrorist cells, criminal gangs, military platoons, sports teams and conferences, work groups etc. [...]

[...]

Some direct application areas of social networks include studying terrorist networks [43,9], which is essentially a special application of criminal network analysis that is intended to study organized crimes such as terrorism, drug trafficking and money laundering [36,21]. Concepts of social network analysis provide suitable data mining tools for this purpose [17]. Figure 1 shows an example of a terrorist network, which maps the links between terrorists involved in the tragic events of September 11, 2001. This graph was constructed in [32] using the public data that were available before, but collected after the event. Even though the information mapped in this network is by no means complete, its analysis may still provide valuable insights into the structure of a terrorist organization.


9. Berry, N., Ko, T., Moy, T., Smrcka, J., Turnley, J., Wu, B.: Emergent clique formation in terrorist recruitment. The AAAI-04 Workshop on Agent Organizations: Theory and Practice, July 25, 2004, San Jose, California (2004). Http://www.cs.uu.nl/ virginia/aotp/papers.htm [sic]

17. Chen, H., Chung, W., Xu, J.J., Wang, G., Qin, Y., Chau, M.: Crime data mining: A general framework and some examples. Computer 37(4), 50–56 (2004)

21. Davis, R.H.: Social network analysis: An aid in conspiracy investigations. FBI Law Enforcement Bulletin pp. 11–19 (1981)

32. Krebs, V.: Mapping networks of terrorist cells. Connections 24, 45–52 (2002)

36. McAndrew, D.: The structural analysis of criminal networks. In: D. Canter, L. Alison (eds.) The Social Psychology of Crime: Groups, Teams, and Networks, Offender Profiling Series, III. Aldershot, Dartmouth (1999)

43. Sageman, M.: Understanding Terrorist Networks. University of Pennsylvania Press (2004)

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The source is not given. The copied text starts on the previous page: Nm3/Fragment_1037_35. Figure 1 is different in each text.

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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)

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These drawbacks are pointed out and the models are appropriately redefined in (Balasundaram, B. et al, 2005). All these models emphasize the need for high reachability inside a cohesive subgroup and have their own merits and demerits as models of cohesiveness. In this paper we also discuss on a degree based model and called k-plex (Wasserman, S. et al, 2004). This model relaxes familiarity within a cohesive subgroup and implicitly provides reachability and robustness. These drawbacks are pointed out and the models are appropriately redefined in [7], as described in Section 2. All these models emphasize the need for high reachability inside a cohesive subgroup and have their own merits and demerits as models of cohesiveness. The focus of this paper is on a degree based model introduced in [47] and called k-plex. This model relaxes familiarity within a cohesive subgroup and implicitly provides reachability and robustness.

7. Balasundaram, B., Butenko, S., Trukhanov, S.: Novel approaches for analyzing biological networks. Journal of Combinatorial Optimization 10, 23–39 (2005)

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

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