Hypergraph Laplacians in Diffusion Framework

Mehmet Emin Aktas; Esra Akbas

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arXiv · 2102.08867

Hypergraph Laplacians in Diffusion Framework

Mehmet Emin Aktas·Esra Akbas

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Abstract

Networks are important structures used to model complex systems where interactions take place. In a basic network model, entities are represented as nodes, and interaction and relations among them are represented as edges. However, in a complex system, we cannot describe all relations as pairwise interactions, rather should describe as higher-order interactions. Hypergraphs are successfully used to model higher-order interactions in complex systems. In this paper, we present two new hypergraph Laplacians based on diffusion framework. Our Laplacians take the relations between higher-order interactions into consideration, hence can be used to model diffusion on hypergraphs not only between vertices but also higher-order structures. These Laplacians can be employed in different network mining problems on hypergraphs, such as social contagion models on hypergraphs, influence study on hypergraphs, and hypergraph classification, to list a few.

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Mehmet Emin Aktas, Esra Akbas. 2021-02-17. Hypergraph Laplacians in Diffusion Framework. https://arxiv.org/abs/2102.08867

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