Name
Abstract | ||
|---|---|---|
In this contribution, we represent hypergraphs as partially ordered sets or posets, and provide a geometric framework based on posets to compute the Forman-Ricci curvature of vertices as well as hyperedges in hypergraphs. Specifically, we first provide a canonical method to construct a two-dimensional simplicial complex associated with a hypergraph, such that the vertices of the simplicial complex represent the vertices and hyperedges of the original hypergraph. We then define the Forman-Ricci curvature of the vertices and the hyperedges as the scalar curvature of the associated vertices in the simplicial complex. Remarkably, Forman-Ricci curvature has a simple combinatorial expression and it can effectively capture the variation in symmetry or asymmetry over a hypergraph. Finally, we perform an empirical study involving computation and analysis of the Forman-Ricci curvature of hyperedges in several real-world hypergraphs. We find that Forman-Ricci curvature shows a moderate to high absolute correlation with standard hypergraph measures such as eigenvector centrality and cardinality. Our results suggest that the notion of Forman-Ricci curvature extended to hypergraphs in this work can be used to gain novel insights on the organization of higher-order interactions in real-world hypernetworks. |
Year | DOI | Venue |
|---|---|---|
2022 | 10.3390/sym14020420 | SYMMETRY-BASEL |
Keywords | DocType | Volume |
hypergraph, poset, simplicial complex, Forman-Ricci curvature, higher-order interactions | Journal | 14 |
Issue | ISSN | Citations |
2 | 2073-8994 | 0 |
PageRank | References | Authors |
0.34 | 0 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Yasharth Yadav | 1 | 0 | 0.34 |
| Areejit Samal | 2 | 0 | 0.34 |
| Emil Saucan | 3 | 77 | 18.84 |