Core-periphery Models for Hypergraphs

• URL: http://arxiv.org/abs/2206.00783v1
• Date: Wed, 1 Jun 2022 22:11:44 GMT
• Title: Core-periphery Models for Hypergraphs
• Authors: Marios Papachristou, Jon Kleinberg
• Abstract summary: We introduce a random hypergraph model for core-periphery structure. We develop a novel statistical inference algorithm that is able to scale to large hypergraphs with runtime that is practically linear wrt. Our inference algorithm is capable of learning embeddings that correspond to the reputation (rank) of a node within the hypergraph.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We introduce a random hypergraph model for core-periphery structure. By leveraging our model's sufficient statistics, we develop a novel statistical inference algorithm that is able to scale to large hypergraphs with runtime that is practically linear wrt. the number of nodes in the graph after a preprocessing step that is almost linear in the number of hyperedges, as well as a scalable sampling algorithm. Our inference algorithm is capable of learning embeddings that correspond to the reputation (rank) of a node within the hypergraph. We also give theoretical bounds on the size of the core of hypergraphs generated by our model. We experiment with hypergraph data that range to $\sim 10^5$ hyperedges mined from the Microsoft Academic Graph, Stack Exchange, and GitHub and show that our model outperforms baselines wrt. producing good fits.

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