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

von Nasrullah Memon

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[1.] Nm/Fragment 104 02 - Diskussion
Zuletzt bearbeitet: 2012-05-22 19:21:30 Hindemith
Fragment, Gesichtet, Nm, SMWFragment, Schutzlevel sysop, Stephenson and Zelen 1989, Verschleierung

Typus
Verschleierung
Bearbeiter
Graf Isolan
Gesichtet
Yes.png
Untersuchte Arbeit:
Seite: 103, Zeilen: 2-8
Quelle: Stephenson and Zelen 1989
Seite(n): 3, Zeilen: 10-16
The third measure is called betweenness and is the frequency at which a node occurs on a geodesic that connects a pair 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” (Frantz, T. and K. M. Carley, 2005). 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).
Anmerkungen

nothing is marked as a citation, the source remains unnamed.

Sichter
(Graf Isolan), Hindemith

[2.] Nm/Fragment 104 12 - Diskussion
Zuletzt bearbeitet: 2012-05-19 14:06:21 Graf Isolan
Fragment, Gesichtet, Koschuetzki etal 2005, Nm, SMWFragment, Schutzlevel sysop, Verschleierung

Typus
Verschleierung
Bearbeiter
Hindemith, Graf Isolan
Gesichtet
Yes.png
Untersuchte Arbeit:
Seite: 104, Zeilen: 12-24
Quelle: Koschuetzki_etal_2005
Seite(n): 29-30, Zeilen: p29: 26ff; p30: 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 s and t. 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 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:

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 thesis anywhere.

Telling mistake: indeed, in his definition Nm writes "where \sigma_{uw} denotes the number of all shortest-paths between s and t.", thus mistakenly referring to the name of the nodes in the original text.

Sichter
(Hindemith), Bummelchen


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