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.
The harmonic index of a graphGis the sum of weights2/(du +d v)of all edges(u, v)ofG, whered u denotes the degree of a nodeuinG
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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.