We propose a one-parameter family of random walk processes on hypergraphs, where a parameter biases the dynamics of the walker towards hyperedges of low or high cardinality. We show that for each value of the parameter, the resulting process defines its own hypergraph projection on a weighted network. We then explore the differences between them by considering the community structure associated to each random walk process. To do so, we adapt the Markov stability framework to hypergraphs and test it on artificial and real-world hypergraphs.

中文翻译：

---

超图中的随机游走和社区检测

我们在超图上提出了一个单参数系列的随机游走过程，其中一个参数使步行者的动态偏向于低基数或高基数的超边。我们表明，对于参数的每个值，结果过程在加权网络上定义了自己的超图投影。然后我们通过考虑与每个随机游走过程相关的社区结构来探索它们之间的差异。为此，我们将马尔可夫稳定性框架应用于超图，并在人工和真实世界的超图上对其进行测试。