# Nm2/436

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How Investigative Data Mining Can Help Intelligence Agencies to Discover Dependence of Nodes in Terrorist Networks

von Nasrullah Memon, David L. Hicks, Henrik Legind Larsen

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 Zuletzt bearbeitet: 2014-01-11 22:28:47 WiseWoman Fragment, Gesichtet, KomplettPlagiat, Koschuetzki et al 2005, Nm2, SMWFragment, Schutzlevel sysop

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The degree centrality Cd(v) of a vertex v is simply defined as the degree d(v) of v if the considered graph is undirected. The degree centrality is, e.g., applicable whenever the graph represents something like a voting result. These networks represent a static situation and we are interested in the vertex that has the most direct votes or that can reach most other vertices directly. The degree centrality is a local measure, because the centrality value of a vertex is only determined by the number of its neighbors. The most simple centrality is the degree centrality cD(v) of a vertex v that is simply defined as the degree d(v) of v if the considered graph is undirected. [...] The degree centrality is, e.g., applicable whenever the graph represents something like a voting result. These networks represent a static situation and we are interested in the vertex that has the most direct votes or that can reach most other vertices directly. The degree centrality is a local measure, because the centrality value of a vertex is only determined by the number of its neighbors.
 Anmerkungen The source is not mentioned anywhere in the paper. Sichter (Hindemith), WiseWoman

 Zuletzt bearbeitet: 2014-01-12 10:20:16 Singulus Fragment, Gesichtet, Koschuetzki et al 2005, Nm2, SMWFragment, Schutzlevel sysop, Verschleierung

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We denote the sum of the distances from a vertex u ∈ V to any other vertex in a graph G = (V,E) as the total distance $\sum_{u\in V}d(u,v)$, where d(u,v) is shortest [sic] distance between the nodes u and v The problem of finding an appropriate location can be solved by computing the set of vertices with minimum total distance.

In SNA literature, a centrality measure based on this concept is called closeness. The focus lies here, for example, on measuring the closeness of a person to all other people in the network. People with a small total distance are considered as most important as those with high total distance. The most commonly employed definition of closeness is the reciprocal of the total distance:

$C_{C}(u)=\frac{1}{\sum_{v\in V}d(u,v)}\qquad (2)$

$C_{C}(u)$ grows with decreasing total distance of u, therefore it is also known as a structural index.

We denote the sum of the distances from a vertex u ∈ V to any other vertex in a graph G = (V,E) as the total distance2 $\sum_{v\in V}d(u,v)$. The problem of finding an appropriate location can be solved by computing the set of vertices with minimum total distance. [...]

In social network analysis a centrality index based on this concept is called closeness. The focus lies here, for example, on measuring the closeness of a person to all other people in the network. People with a small total distance are considered as more important as those with a high total distance. [...] The most commonly employed definition of closeness is the reciprocal of the total distance

[page 23]

$C_{C}(u)=\frac{1}{\sum_{v\in V}d(u,v)}\qquad (3.2)$

In our sense this definition is a vertex centrality, since '$C_{C}(u$) grows with decreasing total distance of u and it is clearly a structural index.

2 In [273], Harary used the term status to describe a status of a person in an organization or a group. In the context of communication networks this sum is also called transmission number.

 Anmerkungen The source is not mentioned anywhere in the paper. Sichter (Hindemith), WiseWoman

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