Resistance Distances in Simplicial Networks

Ming-Zhang Zhu, Wanyue Xu, Zhongzhi Zhang, Haibin Kan, Guanrong Chen
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引用次数: 1

Abstract

It is well known that in many real networks, such as brain networks and scientific collaboration networks, there exist higher-order nonpairwise relations among nodes, i.e., interactions between among than two nodes at a time. This simplicial structure can be described by simplicial complexes and has an important effect on topological and dynamical properties of networks involving such group interactions. In this paper, we study analytically resistance distances in iteratively growing networks with higher-order interactions characterized by the simplicial structure that is controlled by a parameter q. We derive exact formulas for interesting quantities about resistance distances, including Kirchhoff index, additive degree-Kirchhoff index, multiplicative degree-Kirchhoff index, as well as average resistance distance, which have found applications in various areas elsewhere. We show that the average resistance distance tends to a q-dependent constant, indicating the impact of simplicial organization on the structural robustness measured by average resistance distance.
简单网络中的阻力距离
众所周知,在许多现实网络中,如大脑网络和科学协作网络,节点之间存在高阶非成对关系,即同时存在两个以上节点之间的相互作用。这种简单结构可以用简单配合物来描述,并且对涉及这种群相互作用的网络的拓扑和动力学性质有重要影响。在本文中,我们解析地研究了具有由参数q控制的简单结构的高阶相互作用的迭代增长网络中的电阻距离。我们导出了关于电阻距离的有趣量的精确公式,包括Kirchhoff指数,加性度-Kirchhoff指数,乘性度-Kirchhoff指数以及平均电阻距离,这些公式在其他各个领域都有应用。我们发现平均阻力距离趋向于q依赖常数,表明简单组织对平均阻力距离测量的结构鲁棒性的影响。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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