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原文連結
論文資訊
- 類型：已發表論文
- 日期：2020-07-27
摘要
Many empirical 網絡s incorporate higher order relations between elements and therefore are naturally modelled as, possibly directed and/or weighted, hypergraphs, rather than merely as graphs. In order to develop a systematic tool for the 統計 analysis of such hypergraph, we propose a general definition of Ricci curvature on directed hypergraphs and explore the consequences of that definition. The definition generalizes Ollivier’s definition for graphs. It involves a carefully designed optimal transport problem between sets of vertices. While the definition looks somewhat complex, in the end we shall be able to express our curvature in a very simple formula, κ = μ0 − μ2 − 2μ3. This formula simply counts the fraction of vertices that have to be moved by distances 0, 2 or 3 in an optimal transpor
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