## FANDOM

33.178 Seiten

 Typus Verschleierung Bearbeiter Hindemith Gesichtet
Untersuchte Arbeit:
Seite: 436, Zeilen: 28-39
Quelle: Koschuetzki et al 2005
Seite(n): 22, 23, Zeilen: 22: 12ff; 23: 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 $\sum_{u\in V}d(u,v)$, where d(u,v) is shortest [sic] distance between the nodes u and v The problem of finding an appropriate location can be solved by computing the set of vertices with 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 most 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 a 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 distance2 $\sum_{v\in V}d(u,v)$. 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 '$C_{C}(u$) grows with decreasing total distance of u and it is clearly a structural index.

2 In [273], Harary used the term status to describe a status of a person in an organization or a group. In the context of communication networks this sum is also called transmission number.

 Anmerkungen The source is not mentioned anywhere in the paper. Sichter (Hindemith), WiseWoman