# Nm2/437

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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 22:03:33 WiseWoman Fragment, Gesichtet, Nm2, SMWFragment, Schutzlevel sysop, Stephenson and Zelen 1989, Verschleierung

 Typus Verschleierung Bearbeiter Hindemith Gesichtet
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Quelle: Stephenson and Zelen 1989
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The third measure is betweenness which is defined as the frequency at which a node occurs on geodesics that connect pairs of nodes. Thus, any node that falls on the shortest path between other nodes can potentially control the transmission of information or effect exchange by being an intermediary; it is the potential for control that defines the centrality of these nodes [23].

23. Freeman, L.C., Freeman, S.C., Michaelson, A.G.: On Human Social Intelligence. Journal of Social and Biological Structures 11, 415–425 (1988)

The third measure is called betweenness and is the frequency at which a point occurs on the geodesic that connects pairs of points. Thus, any point that falls on the shortest path between other points can potentially control the transmission of information or effect exchange by being an intermediary. “It is this potential for control that defines the centrality of these points” (Freeman 1979a: 221).

Freeman, L.C. 1979 a “Centrality in Social Networks: Conceptual Clarification.” Social Networks I: 215-239.

 Anmerkungen The authors replace "point" with "node" and remove the quotation marks of the Freeman quote, although a different Freeman paper is cited that does not actually discuss "betweenness" at all. Stephenson & Zelen (1989) are not mentioned. Sichter (Hindemith), WiseWoman

 Zuletzt bearbeitet: 2014-01-12 10:23:42 Singulus Fragment, Gesichtet, Koschuetzki et al 2005, Nm2, SMWFragment, Schutzlevel sysop, Verschleierung

 Typus Verschleierung Bearbeiter Hindemith Gesichtet
Untersuchte Arbeit:
Seite: 437, Zeilen: 9-19
Quelle: Koschuetzki et al 2005
Seite(n): 29-30, Zeilen: 29: 26ff; 30: 1, 13-15
Let $\delta_{uw}(v)$ denotes the fraction of shortest paths between u and w that contain vertex v:

$\delta_{uw}(v)=\frac{\sigma_{uw}(v)}{\sigma_{uw}}\quad (3)$

where $\sigma_{uw}$ denotes the number of all shortest-paths between u and w. The ratio $\delta_{uw}(v)$ can be interpreted as the probability that vertex v is involved into any communication between u and w. Note, that the measure implicitly assumes that all communication is conducted along shortest paths. Then the betweenness centrality $C_{B}(v)$ of a vertex v is given by:

$C_{B}(v)=\sum_{u\neq v\in V}\sum_{w\neq v\in V}\delta_{uw}(v)\quad (4)$

Any pair of vertices u and w without any shortest path from u to w will add zero to the betweenness centrality of every other vertex in the network.

Let $\delta_{st}(v)$ denote the fraction of shortest paths between s and t that contain vertex v:

$\delta_{st}(v)=\frac{\sigma_{st}(v)}{\sigma_{st}}\quad (3.12)$

where $\sigma_{st}$ denotes the number of all shortest-path [sic] between s and t. Ratios $\delta_{st}(v)$ can be interpreted as the probability that vertex v is involved into any communication between s and t. Note, that the index implicitly assumes that all communication is conducted along shortest paths. Then the betweenness centrality $c_{B}(v)$ of a vertex v is given by:

[page 30]

$c_{B}(v)=\sum_{s\neq v\in V}\sum_{t\neq v\in V}\delta_{st}(v)\quad (3.13)$

[...]

Any pair of vertices s and t without any shortest path from s to t just will add zero to the betweenness centrality of every other vertex in the network.

 Anmerkungen The definitions given here are, of course, standard and don't require a citation. However, the interpreting and explaining text is taken from the source word for word. The source is not mentioned in the paper anywhere. Sichter (Hindemith), WiseWoman

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