Class of models for random hypergraphs
Class of models for random hypergraphs
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DOI：
10.1103/physreve.106.064310
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发表时间：
2022-12-16
影响因子：
2.4
通讯作者：
Barthelemy, Marc
中科院分区：
文献类型：
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作者：
Barthelemy, Marc
尽管最近表现出的重要性，高阶相互作用的各种过程中，很少有灵活的（空）模型。特别是，大多数超图的研究集中在一个小的理论模型。在这里，我们介绍了一类随机超图模型，它显示了类似的复杂网络模型的灵活性水平，其中的主要成分是一个节点属于超边缘的概率。当这个概率是一个常数，我们得到一个随机超图在相同的精神作为Erdos-Renyi图。这个框架还允许我们引入不同的成分，如超图或空间随机超图的优先连接。特别地，我们证明了对于Erdos-Renyi情况，存在一个转变阈值缩放为1/./其中N是节点数，E是超边数。我们还讨论了一个随机的几何超图，它显示了一个阈值距离标度为rc* 类似于1/。E.对于这些不同的模型，我们提供了最有趣的措施的结果，并介绍了新的空间的情况下，表征超边的几何性质。这些不同的模型可以作为分析经验数据的基准。
Despite the recently exhibited importance of higher-order interactions for various processes, few flexible (null) models are available. In particular, most studies on hypergraphs focus on a small set of theoretical models. Here, we introduce a class of models for random hypergraphs which displays a similar level of flexibility of complex network models and where the main ingredient is the probability that a node belongs to a hyperedge. When this probability is a constant, we obtain a random hypergraph in the same spirit as the Erdos-Renyi graph. This framework also allows us to introduce different ingredients such as the preferential attachment for hypergraphs, or spatial random hypergraphs. In particular, we show that for the Erdos-Renyi case there is a transition threshold scaling as 1/./EN where N is the number of nodes and E the number of hyperedges. We also discuss a random geometric hypergraph which displays a percolation transition for a threshold distance scaling as rc* similar to 1/./E. For these various models, we provide results for the most interesting measures, and also introduce new ones in the spatial case for characterizing the geometrical properties of hyperedges. These different models might serve as benchmarks useful for analyzing empirical data.