Resistance Distances in Simplicial Networks

TL;DR

This paper analytically investigates resistance distances in growing networks with higher-order interactions modeled by simplicial complexes, deriving formulas for key metrics and revealing how simplicial structure influences network robustness.

Contribution

It provides exact formulas for resistance distance metrics in simplicial complex networks and analyzes how higher-order interactions affect network robustness.

Findings

Average resistance distance approaches a q-dependent constant.

Simplicial organization impacts structural robustness.

Derived formulas apply to various network analysis areas.

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.