  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.
