论文标题
基于熵的模型，以随机化现实世界超图
Entropy-based models to randomize real-world hypergraphs
论文作者
论文摘要
网络理论通常忽略了多体关系，仅专注于成对相互作用：但是，忽略它们可能会导致复杂系统的误导性表示。 HyperGraphs代表了描述多边形相互作用的合适框架。在这里，我们利用基于发射率矩阵的超图的表示来扩展基于熵的高阶结构方法：与指数随机图相比，我们介绍了指数的随机超图（ERHS）。在探索阈值概括渗透率的渐近行为之后，我们将ERHS应用于研究现实世界数据。首先，我们将关键网络指标推广到超图；然后，我们计算其期望值并将其与经验值进行比较，以检测与随机行为的偏差。我们的方法在分析上是可扩展的，可扩展的，并且能够揭示现实世界中超图的结构模式，这些模式与较简单的约束而与出现的方法显着不同。
Network theory has often disregarded many-body relationships, solely focusing on pairwise interactions: neglecting them, however, can lead to misleading representations of complex systems. Hypergraphs represent a suitable framework for describing polyadic interactions. Here, we leverage the representation of hypergraphs based on the incidence matrix for extending the entropy-based approach to higher-order structures: in analogy with the Exponential Random Graphs, we introduce the Exponential Random Hypergraphs (ERHs). After exploring the asymptotic behaviour of thresholds generalising the percolation one, we apply ERHs to study real-world data. First, we generalise key network metrics to hypergraphs; then, we compute their expected value and compare it with the empirical one, in order to detect deviations from random behaviours. Our method is analytically tractable, scalable and capable of revealing structural patterns of real-world hypergraphs that differ significantly from those emerging as a consequence of simpler constraints.
