Traversa Pietro, de Arruda Guilherme Ferraz, Moreno Yamir
Institute for Biocomputation and Physics of Complex Systems (BIFI), University of Zaragoza, 50018 Zaragoza, Spain.
Department of Theoretical Physics, University of Zaragoza, 50018 Zaragoza, Spain.
Phys Rev E. 2024 May;109(5-1):054309. doi: 10.1103/PhysRevE.109.054309.
Random walks have been intensively studied on regular and complex networks, which are used to represent pairwise interactions. Nonetheless, recent works have demonstrated that many real-world processes are better captured by higher-order relationships, which are naturally represented by hypergraphs. Here we study random walks on hypergraphs. Due to the higher-order nature of these mathematical objects, one can define more than one type of walks. In particular, we study the unbiased and the maximal entropy random walk on hypergraphs with two types of steps, emphasizing their similarities and differences. We characterize these dynamic processes by examining their stationary distributions and associated hitting times. To illustrate our findings, we present a toy example and conduct extensive analyses of artificial and real hypergraphs, providing insights into both their structural and dynamical properties. We hope that our findings motivate further research extending the analysis to different classes of random walks as well as to practical applications.
随机游走已在正则网络和复杂网络上得到深入研究，这些网络用于表示成对的相互作用。尽管如此，最近的研究表明，许多现实世界的过程可以通过高阶关系更好地捕捉，而超图自然地表示了这些高阶关系。在此，我们研究超图上的随机游走。由于这些数学对象的高阶性质，可以定义不止一种类型的游走。特别地，我们研究具有两种步长的超图上的无偏随机游走和最大熵随机游走，强调它们的异同。我们通过研究它们的平稳分布和相关的击中时间来刻画这些动态过程。为了说明我们的发现，我们给出一个简单示例，并对人工超图和真实超图进行广泛分析，从而深入了解它们的结构和动态特性。我们希望我们的发现能激发进一步的研究，将分析扩展到不同类型的随机游走以及实际应用中。
