Nm/103

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

von Nasrullah Memon

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[1.] Nm/Fragment 103 15 - Diskussion
Zuletzt bearbeitet: 2012-04-29 22:07:40 Hindemith

Fragment, Gesichtet, Koschuetzki etal 2005, Nm, SMWFragment, Schutzlevel sysop, Verschleierung

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 
  
          ∑
          
            v
            ∈
            V
          
        d
        (
        u
        ,
        v
        )
      
    {\displaystyle \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
        )
        =
        
          1
          
              ∑
              
                v
                ∈
                V
              
            d
            (
            u
            ,
            v
            )
          
        (
        2
        )
      
    {\displaystyle C_{C}(u)=\frac{1}{\sum_{v\in V}d(u,v)}\qquad (2)}
  
          C
          
            C
          
        (
        u
        )
      
    {\displaystyle 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] 
  
          ∑
          
            v
            ∈
            V
          
        d
        (
        u
        ,
        v
        )
      
    {\displaystyle \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
        )
        =
        
          1
          
              ∑
              
                v
                ∈
                V
              
            d
            (
            u
            ,
            v
            )
          
        (
        3.2
        )
      
    {\displaystyle 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

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