'Advanced Network Analysis / Pajek: Large ... - Vladimir Batagelj

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V. Batagelj: Analysis and visulization of large networks with Pajek 51 ✬ Clustering coefficient Let G = (V, E) be simple undirected graph. Clustering in vertex v is usually measured as a quotient between the number of lines in subgraph G 1 (v) = G(N 1 (v)) induced by the neighbors of vertex v and the number of lines in the complete graph on these vertices: C(v) = ⎧ ⎪⎨ ⎪⎩ 2|L(G 1 (v))| deg(v)(deg(v) − 1) deg(v) > 1 0 otherwise We can consider also the size of vertex neighborhood by the following correction C1(v) = deg(v) ∆ C(v) where ∆ is the maximum degree in graph G. This measure attains its largest value in vertices that belong to an isolated clique of size ∆. ✫ Methodenforum der Fakultät für Sozialwissenschaften, Universität Wien, 21-22. 6. 2007 ▲ ❙ ▲ ▲ ▲ ● ❙ ▲ ▲ ☛ ✖ ✩ ✪
V. Batagelj: Analysis and visulization of large networks with Pajek 52 ✬ ✫ Dense groups Several notions were proposed in attempts to formally describe dense groups in graphs. Clique of order k is a maximal complete subgraph (isomorphic to Kk), k ≥ 3. s-plexes, LS sets, lambda sets, cores, . . . For all of them, except for cores, it turned out that they are difficult to detemine. Methodenforum der Fakultät für Sozialwissenschaften, Universität Wien, 21-22. 6. 2007 ▲ ❙ ▲ ▲ ● ❙ ▲ ▲ ☛ ✖ ▲ ✩ ✪
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'Advanced Network Analysis / Pajek: Large ... - Vladimir Batagelj

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