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Investigative Data Mining: Mathematical Models for Analyzing, Visualizing and Destabilizing Terrorist Networks

von Nasrullah Memon

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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)

 Anmerkungen 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). Sichter (Hindemith), Graf Isolan

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