Cycle-density filtrations based on motif densities enable persistent homology to distinguish non-isomorphic graphs nearly perfectly and achieve strong performance on real-world graph property prediction.
If T(v)is the number of triangles containing a node vandd v is the degree ofv, then the clustering coefficient [16] isC(v) = 2T(v)/(d v(dv −1))
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Motif-based filtrations for persistent homology: A framework for graph isomorphism and property prediction
Cycle-density filtrations based on motif densities enable persistent homology to distinguish non-isomorphic graphs nearly perfectly and achieve strong performance on real-world graph property prediction.