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    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|α(|V|)), where a 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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    The Reeb graph of a scalar function that is defined on a domain gives a topologically meaningful summary of that domain. Reeb graphs have been shown in the past decade to be of great importance in geometric processing, image processing, computer graphics, and computational topology. The demand for analyzing large data sets has increased in the last decade. Hence, the parallelization of topological computations needs to be more fully considered. We propose a parallel augmented Reeb graph algorithm on triangulated meshes with and without a boundary. That is, in addition to our parallel algorithm for computing a Reeb graph, we describe a method for extracting the original manifold data from the Reeb graph structure. We demonstrate the running time of our algorithm on standard datasets. As an application, we show how our algorithm can be utilized in mesh segmentation algorithms. 
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