In this project, we study how stochastic processes behave on graph. The main idea is to generate many random signals and to filter them (thanks to spectral graph theory). The output of this operation tells a lot about the graph itself. First, it gives local regularity information: is some node more connected to the other? Or isolated? Second, thanks to this technique, we can compute the density of the Laplacian’s eigenvalues of the graphs. This allows a graph classification for instance. Third, we can even perform this classification for a specific node. Finally, the algorithm used in this project scales to very large graphs. We should be able to analyze a big instance of a social network.

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