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.
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 article, we use the PageRank function along with persistent homology to obtain a scalable graph descriptor and utilize it to compare the similarities between graphs. For a given graph G(V,E), our descriptor can be computed in O(|E|\alpha(|V|)), where \alpha is the inverse Ackermann function which makes it scalable and computable on massive graphs . We show the effectiveness of our method by utilizing it on multiple shape mesh datasets.
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study the problem of graph similarity. By representing each graph as a persistence diagram,we can then compare outputs using the bottleneck distance
obtain a scalable graph descriptor and utilize it to compare the similarities between graphs. For a given graph G(V,E), our descriptor can be computed in O(|E|\alpha(|V|)), where \alpha is the inverse Ackermann function which makes it scalable and computable on massive graphs
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