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Fig. 2 | Journal of Cheminformatics

Fig. 2

From: How frequently do clusters occur in hierarchical clustering analysis? A graph theoretical approach to studying ties in proximity

Fig. 2

Relaxed graph-cluster contrast \(CC_{rg}\) accounts for more details than graph-cluster contrast \(CC_g\). In this example C is not a subtree of \(D_i\), leading to \(CC_{g}=0\). Nevertheless, C and \(D_i\) share a subtree named \(g_1\), leading to \(CC_{rg}>0\); in fact, they share one out of three subtrees having \(CC_{rg}=1/3\). Regarding the set-cluster contrast functions for this example, we have \(CC_{s}=1\) meaning a perfect match between the set of leaves of C and one of the leaves of one branch (subtree) of \(D_i\) i.e. \(L(C)=s_3\), implying that \(CC_{rs}\) is also 1

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