Abstract
The technique of measuring similarity between topological spaces using Wasserstein distance
 between persistence diagrams is extended to graph networks in this paper. A relationship
 between the Wasserstein distance of the Cartesian product of topological spaces and the
 Wasserstein distance of individual spaces is found to ease the comparative study of the
 Cartesian product of topological spaces. The Cartesian product and the strong product of
 weighted graphs are defined, and the relationship between the Wasserstein distance between
 graph products and the Wasserstein distance between individual graphs is determined. For
 this, clique complex filtration and the Vietoris- Rips filtration are used.
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