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

V. Batagelj: Analysis and visulization of large networks with Pajek 106
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. . . Networks from data tables
Suppose that the property q has the range Q. If Q is finite (it can always be
transformed in such set by partitioning the set Q and recoding the values)
we can assign to the property q a two-mode network K ×q = (K, Q, E, w)
where (k, v) ∈ E iff q(k) = v, and w(k, v) = 1.
Also, for properties qi and qj we can define a two-mode network qi ×qj =
(Qi, Qj, E, w) where (u, v) ∈ E iff ∃k ∈ K : (qi(k) = u ∧ qj(k) = v),
and w(u, v) = card({k ∈ K : (qi(k) = u ∧ qj(k) = v)}).
We define [qi × qj] T = qj × qi.
It holds qi × qj = [K × qi] T ∗ [K × qj] = [qi × K] ∗ [K × qj].
We can join a pair of properties qi and qj also with respect to the third
property qs: we get a two-mode network [qi×qj]/qs = [qi×qs]∗[qs×qj].
Methodenforum der Fakultät für Sozialwissenschaften, Universität Wien, 21-22. 6. 2007 ▲
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