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

V. Batagelj: Analysis and visulization of large networks with Pajek 84
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Bipartite cores
The subset of vertices C ⊆ V is a (p, q)-core in a bipartite (2-mode)
network N = (V1, V2; L), V = V1 ∪ V2 iff
a. in the induced subnetwork K = (C1, C2; L(C)), C1 = C ∩ V1, C2 =
C ∩ V2 it holds ∀v ∈ C1 : deg K(v) ≥ p and ∀v ∈ C2 : deg K(v) ≥ q ;
b. C is the maximal subset of V satisfying condition a.
Properties of bipartite cores:
• C(0, 0) = V
• K(p, q) is not always connected
• (p1 ≤ p2) ∧ (q1 ≤ q2) ⇒ C(p1, q1) ⊆ C(p2, q2)
• C = {C(p, q) : p, q ∈ N}. If all nonempty elements of C are different
it is a lattice.
Methodenforum der Fakultät für Sozialwissenschaften, Universität Wien, 21-22. 6. 2007 ▲
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