Model of Simplicial Complexes with dimension-wise preferential attachment
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.
Versions
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BibTeX
@misc{febbe2026model,
title = {{Model of Simplicial Complexes with dimension-wise preferential attachment}},
author = {Diego Febbe and Duccio Fanelli and Timoteo Carletti},
howpublished = {arXiv},
year = {2026},
month = jul,
doi = {10.48550/arxiv.2605.17004},
eprint = {2605.17004},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.17004},
}
RIS
TY - UNPB
TI - Model of Simplicial Complexes with dimension-wise preferential attachment
AU - Diego Febbe
AU - Duccio Fanelli
AU - Timoteo Carletti
PY - 2026
DA - 2026/07/25
PB - arXiv
DO - 10.48550/arxiv.2605.17004
UR - https://arxiv.org/abs/2605.17004
AB - 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.
ER -