'Advanced Network Analysis / Pajek: Large ... - Vladimir Batagelj
'Advanced Network Analysis / Pajek: Large ... - Vladimir Batagelj
'Advanced Network Analysis / Pajek: Large ... - Vladimir Batagelj
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V. <strong>Batagelj</strong>: <strong>Analysis</strong> and visulization of large networks with <strong>Pajek</strong> 51<br />
✬<br />
Clustering coefficient<br />
Let G = (V, E) be simple undirected graph. Clustering in vertex v is<br />
usually measured as a quotient between the number of lines in subgraph<br />
G 1 (v) = G(N 1 (v)) induced by the neighbors of vertex v and the number of<br />
lines in the complete graph on these vertices:<br />
C(v) =<br />
⎧<br />
⎪⎨<br />
⎪⎩<br />
2|L(G 1 (v))|<br />
deg(v)(deg(v) − 1)<br />
deg(v) > 1<br />
0 otherwise<br />
We can consider also the size of vertex neighborhood by the following<br />
correction<br />
C1(v) = deg(v)<br />
∆ C(v)<br />
where ∆ is the maximum degree in graph G. This measure attains its largest<br />
value in vertices that belong to an isolated clique of size ∆.<br />
✫<br />
Methodenforum der Fakultät für Sozialwissenschaften, Universität Wien, 21-22. 6. 2007 ▲<br />
❙ ▲<br />
▲<br />
▲<br />
● ❙ ▲<br />
▲<br />
☛ ✖<br />
✩<br />
✪
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