Model of simplicial complexes with dimension wise preferential attachment

Network science is a powerful framework allowing to model complex systems, capable to describe and take into account the intricate web of connections existing among the constituting basic elements of the system. Recently scholars have brought to the fore the relevance of higher-order networks, namely structures allowing to encode for many-body interactions, differently from the pairwise case handled by networks. This novel research field opens new avenues of research with applications ranging from neuroscience to social sciences and beyond; there is thus a need for generative models of higher-order networks 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, whose exponent has been analytically determined by studying the growth process and explicitly depends on the probability to add simplices of a given dimension.