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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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