The topology of the directed clique complex as a network invariant

Understand

We introduce new algebro-topological invariants of directed networks, based on the topological construction of the directed clique complex.

• The shape of the underlying directed graph is encoded in a way that can be studied mathematically to obtain network invariants such as the Euler characteristic and the Betti numbers.
• Two different cases illustrate the application of the Euler characteristic.
• We investigate how the evolution of a Boolean recurrent artificial neural network is influenced by its topology in a dynamics involving pruning and strengthening of the connections, and to show that the topological features of the directed clique complex influence the dynamical evolution of the network.