Frustration vs . Clusterability in Two - Mode Signed Networks ( Signed Bipartite Graphs )
نویسنده
چکیده
Mrvar and Doreian recently defined a notion of bipartite clustering in bipartite signed graphs that gives a measure of imbalance of the signed graph, different from previous measures (the “frustration index” or “line index of balance”, l, and Davis’s clusterability). A biclustering of a bipartite signed graph is a pair (π1, π2) of partitions of the two color classes; the sets of the partitions are called clusters. The majority biclusterability index M(k1, k2) is the minimum number of edges that are inconsistent, in a certain definition, with a biclustering, over all biclusterings with |π1| = k1 and |π2| = k2. Theorems: M(1, k2) ≥ l, while M(k1, k2) ≤ l if k1, k2 ≥ 2. For K2,n with n ≥ 2, M(2, 2) = l in about 1/3 of all signatures. If n > 2, then for every signature of K2,n there exists a biclustering with |π1| = |π2| = 2 such that M(π1, π2) = l. There are many open questions.
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