Graph Similarity Using PageRank and Persistent Homology

The PageRank of a graph is a scalar function defined on the node set of the graph which encodes nodes centrality information of the graph. In this work, we utilize the PageRank function on the lower-star filtration of the graph as input to persistent homology to study the problem of graph similarity. By representing each graph as a persistence diagram, we can then compare outputs using the bottleneck distance. We show the effectiveness of our method by utilizing it on two shape mesh datasets.