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

V. Batagelj: Analysis and visulization of large networks with Pajek 56
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Generalized cores
The notion of core can be generalized to networks. Let N = (V, E, w)
be a network, where G = (V, E) is a graph and w : E → R is a function
assigning values to edges. A vertex property function on N, or a pfunction
for short, is a function p(v, U), v ∈ V, U ⊆ V with real values.
Let NU (v) = N(v) ∩ U. Besides degrees, here are some examples of
p-functions:
pS(v, U) = �
w(v, u), where w : E → R + 0
u∈NU (v)
pM (v, U) = max w(v, u), where w : E → R
u∈NU (v)
pk(v, U) = number of cycles of length k through vertex v in (U, E|U)
The subgraph H = (C, E|C) induced by the set C ⊆ V is a p-core at level
t ∈ R iff ∀v ∈ C : t ≤ p(v, C) and C is a maximal such set.
Methodenforum der Fakultät für Sozialwissenschaften, Universität Wien, 21-22. 6. 2007 ▲
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