# Weighted Growing Simplicial Complexes

## TL;DR

This paper introduces a non-equilibrium model for weighted growing simplicial complexes, capturing complex interactions across multiple dimensions and revealing how weights influence topology in network structures.

## Contribution

It presents a novel dynamic model for weighted simplicial complexes that accounts for interactions beyond pairwise links and explores weight-topology interplay across dimensions.

## Key findings

- Model generates complex weighted simplicial structures
- Reveals interplay between weights and topology
- Applicable to real-world multi-node interaction networks

## Abstract

Simplicial complexes describe collaboration networks, protein interaction networks and brain networks and in general network structures in which the interactions can include more than two nodes. In real applications, often simplicial complexes are weighted. Here we propose a non-equilibrium model for weighted growing simplicial complexes. The proposed dynamics is able to generate weighted simplicial complexes with a rich interplay between weights and topology emerging not just at the level of nodes and links, but also at the level of faces of higher dimension.