Generalization of triadic closure ** We have seen the definition of the clustering coefficient,…

Generalization of triadic closure ** We have seen the definition of the clustering coefficient, which quantifies the amount of triadic closure. In general, “closure” refers to the intuition that if there are many pairwise connections among a set of nodes, there might be connection for any pair in the set as well. We do not have to limit closure to node-triples as in triadic closure. Here we consider a simple extension called “quad closure.” As shown in Figure 9.14; if node pairs (a,b), (a,c), (a,d), (b, c), and (b, d) are linked, then the pair (c,d) is likely to be linked too. d d – a b a b Figure 9.14 Quad closure: for nodes a, b, c, and d if currently five out of all six possible links exist (left), then the remaining link is likely to appear too (right). To quantify the amount of quad closure, we define a “quad clustering coeffi- cient” as Number of cliques of size 4 Number of connected quadruples with 5 edges/K where K is some normalizing constant. But this definition is incomplete unless we specify the value of K to normalize Q. Find the value of K such that the value of Q for a clique is exactly 1.

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