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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 | Date according to PDF file properties |
| URL | http://www.caam.rice.edu/~ivhicks/kplex.general.pdf |
| Webcite | http://www.webcitation.org/6MzMGGm2A |
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| The Figure 1.4 (in Chapter 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 (2002) using the public data that were available [before, but collected after the event.] | 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. [32]. Krebs, V.: Mapping networks of terrorist cells. Connections 24, 45–52 (2002) |
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| [This graph was constructed by Valdis Krebs (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. | 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.
[32]. Krebs, V.: Mapping networks of terrorist cells. Connections 24, 45–52 (2002) |
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| In the wake of the information revolution, the interest in studying the network structure of organizations, in particular criminal in nature, has increased manifold. Social network concepts, regardless of their flexibility, have come to the forefront especially for these applications. This chapter introduces and studies cohesion analysis of terrorist networks.
Cohesion analysis is often used to explain and develop sociological theories. Members of a cohesive subgroup tend to share information, have homogeneity of thought, identity, beliefs, behaviour, even food habits and illnesses (Wasserman, S., Faust, K., 1994). Social cohesion is also believed to influence emergence of consensus among group members. Examples of cohesive subgroups include religious sects, terrorist groups, criminal gangs/ organized criminals, military teams, and tribal clusters, etc. Some direct application areas of social networks include studying terrorist networks (Sageman, M., 2004; Berry, N. et al., 2004), as mentioned earlier chapters a special application of criminal network analysis. It is anticipated to study organized crimes for example, terrorism, drug trafficking and money laundering, (McAndrew, D.,1999:; Chen, H. et al, 2004)), identity theft, credit card crime, child pornography, human smuggling. It is worthy to mention that SNA concepts provide suitable data mining tools for this purpose (Davis, R.H, 1981). |
In the wake of the information revolution, the interest in studying the network
structure of organizations, in particular criminal in nature, has increased manifold. Social network concepts, despite their versatility, have come to the forefront especially for these applications. [...] [Page 2] 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. 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]. [9]. Berry, N., Ko, T., Moy, T., Smrcka, J., Turnley, J., Wu, B.:[...] (2004). [...] [17]. Chen, H., Chung, W., Xu, J.J., Wang, G., Qin, Y., Chau, M.: [...] (2004) [21]. Davis, R.H.:[...] (1981) [36]. McAndrew, D.: [...] (1999) [43]. Sageman, M.: [...] (2004) [52]. Wasserman, S., Faust, K.: [...] (1994) |
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| It is reported that mathematically modeling a cohesive subgroup has been a subject of interest in social network analysis since many decades.
As stated earlier, 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 nodes. However, the clique approach has been criticized for its [restrictive nature.] |
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 [...]
[35]. Luce, R., Perry, A.: [...] (1949) |
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| [However, the clique approach has been criticized for its] restrictive nature. More details can be found in (Scott, J., 2000; Wasserman, S., Faust, K., 1994) and modeling disadvantages (Seidman, S.B., Foster, B.L., 1978; Freeman, L.C., 1992).
It is important to note that clique models provide three important structural properties that are expected of a cohesive subgroup, namely: 1. familiarity (each node has many neighbours and only a few strangers in the group), 2. reachability (a low diameter, facilitating fast communication between the group members) and 3. robustness (high connectivity, making it difficult to destroy the group by removing members). As mentioned earlier, different models relax different aspects of a cohesive subgroup. In this context, Luce R. introduced a distance based model known as n-clique (Luce, R., 1950). This model was also studied along with a variant called n-clan by Mokken (1979). Some drawbacks are pointed out and the models are appropriately redefined in (Balasundaram, B., Butenko, S., Trukhanov, S., 2005). All these models highlight the need for high reachability inside a cohesive subgroup and have their own advantages and disadvantages as models of cohesiveness. The other variation is degree based model which is known as k-plex (Wasserman, S., Faust, K., 1994). This model relaxes familiarity within a cohesive subgroup and implicitly provides reachability and robustness. |
However, the clique approach has been criticized for its overly restrictive nature [2,52] and modeling disadvantages [47,25].
[...] 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 [...]. These models were also studied along with a variant called k-clan by Mokken [38]. [...] 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. [2]. Alba, R.: [...] (1973) [7]. Balasundaram, B., Butenko, S., Trukhanov, S.:[...] (2005) [25]. Freeman, L.C.: [...] (1992) [34]. Luce, R.:[...] (1950) [38]. Mokken, R.: [...] (1979) [47]. Seidman, S.B., Foster, B.L.: [...] (1978) [52]. Wasserman, S., Faust, K.: [...] (1994) |
The text is copied from the source, which is not given anywhere in the thesis. Some adaptations have taken place, which sometimes did not result in a coherent text (see first paragraph of this fragment). |
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