Model of Simplicial Complexes with dimension-wise preferential attachment

TL;DR

This paper introduces a generative model for higher-order networks called simplicial complexes, using a dimension-wise preferential attachment process to produce power law distributions across different simplex dimensions.

Contribution

It presents a novel model for growing simplicial complexes that captures higher-order interactions with a preferential attachment mechanism across dimensions.

Findings

The model produces power law distributions for generalized degrees.

It captures the growth dynamics of higher-order network structures.

The approach extends traditional network models to simplicial complexes.

Abstract

Network science is a powerful framework allowing to model complex systems, it is capable to describe and take into account the intricate web of connections existing among the constituting basic element of the system. Recently scholars have brought to the fore the relevance of higher-order networks, namely structures allowing to encode for many-body interaction, differently from the pairwise case handled by networks. This novel research field opens new avenues of research with applications ranging from neurosciences to social sciences; there is thus a need for generative models of higher-order network capable to reproduce features present in empirical data. In this work we present a model for growing simplicial complex rooted on a preferential attachment process acting dimension-wise, i.e., returning a power law distribution for the generalized degree of simplexes of different dimension.