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

von Nasrullah Memon

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Statistik und Sichtungsnachweis dieser Seite findet sich am Artikelende
[1.] Nm/Fragment 112 01 - Diskussion
Zuletzt bearbeitet: 2012-04-19 22:38:39 Hindemith
Fragment, Gesichtet, Holmgren 2006, KomplettPlagiat, Nm, SMWFragment, Schutzlevel sysop

Typus
KomplettPlagiat
Bearbeiter
Graf Isolan
Gesichtet
Yes.png
Untersuchte Arbeit:
Seite: 112, Zeilen: 1-27
Quelle: Holmgren 2006
Seite(n): 956-957, Zeilen: p.956, right column 28-45 - p.957, left column 1-18
[Recent studies show that several complex networks have a] heterogeneous topology, i.e., some vertices have a very large number of edges, but the majority of the vertices only have a few edges. That is, the degree distribution follows a power law P(k)\cup k^{-\gamma} for large k(i.e., P(k)/ k^{-\gamma} \to 1 when k\to \infty). The average degree (k) of a graph with N vertices and M edges is (k) = 2M / N.

3.4.2 Clustering Coefficient

Many complex networks exhibit an inherent tendency to cluster. In social networks this represents a circles of friends in which every member knows each other. The clustering coefficient is a local property capturing “the density” of triangles in a graph, i.e., two vertices that both are connected to a third vertex are also directly connected to each other. An i^{th} vertex in a network has k_i edges that connects it to k_i other vertices. The maximum possible number of edges between the k_i neighbours is {k_i \choose 2}=k_i (k_i-1) / 2. The clustering coefficient of i^{th} vertex is defined as the ratio between the number M_i of edges that actually exist between these k_i vertices and the maximum possible number of edges, i.e., C_i = 2 M_i / k_i(k_i-1). The clustering coefficient of the whole network

C = (1/N)\sum_{i=1}^{n}{\mathcal C}_{i} \sum_{i=1}^{n} C_i

3.4.3 Average Path Length

The distance l_{uv} between two vertices u and v is defined as the number of edges along the shortest path connecting them. The average path length l = (l_{uv}) = [1 / N (N - 1)] \sum_{u\neq v\in V}l_{uv} is a measure of how a network is scattered. Sometimes, the diameter d of a graph is defined as the maximum path length between any two connected vertices in the graph. However, in other situations the concept diameter relate to the average path length, i.e., d = l.

[p. 956]

Recent studies show that several complex networks have a heterogeneous topology, i.e., some vertices have a very large number of edges, but the majority of the vertices only have a few edges. That is, the degree distribution follows a power law P(k)\cup k^{-\gamma} for large k(i.e., P(k)/ k^{-\gamma} \to 1 when k\to \infty). The average degree (k) of a graph with N vertices and M edges is (k) = 2M/N.

2.2.2. Clustering Coefficient

Many complex networks exhibit an inherent tendency to cluster. In social networks this represents circles of friends in which every member knows each other. The clustering coefficient is a local property capturing “the density” of triangles in the graph, i.e., two vertices that both are connected to a third vertex are also directly connected to each other. A vertex i in the network has k_i edges that connects it to

[p. 957]

k_i other vertices. The maximum possible number of edges between the ki neighbors is {k_i \choose 2}=k_i(k_i-1)/2. The clustering coefficient of vertex i is defined as the ratio between the number M_i of edges that actually exist between these k_i vertices and the maximum possible number of edges, i.e., C_i = 2 M_i / k_i(k_i-1). The clustering coefficient of the whole network C = (1/N)\sum_i {\mathcal C}_i.

2.2.3. Average Path Length

The distance l_{uv} between two vertices u and v is defined as the number of edges along the shortest path connecting them. The average path length l = (l_{uv}) = [1 / N (N - 1)] \sum_{u\neq v\in V}l_{uv} is a measure of how the network is scattered. Sometimes, the diameter d of a graph is defined as the maximum path length between any two connected vertices in the graph. However, in other situations the concept diameter relate to the average path length, i.e., d = l.

Anmerkungen

The copying process continues with Nm introducing an unfortunate mistake in the formula for the clustering coefficient. Apart from this mistake, both texts are nearly identical.

Sichter
(Graf Isolan), Hindemith


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