Detecting the Coarse Geometry of Networks

Melanie Weber, Jürgen Jost, and Emil Saucan

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Submission date: 16. Nov. 2018 (revised version: November 2018)
Pages: 8
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Abstract:
Clustering and sampling are key methods for the study of relational data. Learning efficient representations of such data relies on the identification of major geometric and topological features and therefore a characterization of its coarse geometry. Here, we introduce an efficient sampling method for identifying crucial structural features using a discrete notion of Ricci curvature. The introduced approach gives rise to a complexity reduction tools that allows for reducing large relational structures (e.g., networks) to a concise core structure on which to focus further, computationally expensive analysis and hypothesis testing.