# Nm/Fragment 103 15

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 Typus Verschleierung Bearbeiter Hindemith Gesichtet
Untersuchte Arbeit:
Seite: 103, Zeilen: 15-27
Quelle: Koschuetzki_etal_2005
Seite(n): 22-23, Zeilen: p22: 12ff; p23: 1-3
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 $\sum_{v\in V}d(u,v)$.

The problem of finding an appropriate location can be solved by computing the set of vertices with a 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 more 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 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 distance [FN 2] $\sum_{v\in V}d(u,v)$. 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 cC(u) grows with decreasing total distance of u and it is clearly a structural index.

 Anmerkungen The source is not mentioned anywhere in the thesis Sichter (Hindemith), Bummelchen