# Nm/Fragment 104 12

31.377Seiten in
diesem Wiki

## Störung durch Adblocker erkannt!

### Wikia ist eine gebührenfreie Seite, die sich durch Werbung finanziert. Benutzer, die Adblocker einsetzen, haben eine modifizierte Ansicht der Seite. Wikia ist nicht verfügbar, wenn du weitere Modifikationen in dem Adblocker-Programm gemacht hast. Wenn du sie entfernst, dann wird die Seite ohne Probleme geladen.

 Typus Verschleierung Bearbeiter Hindemith, Graf Isolan Gesichtet
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