Spectra of the Spike-Flow Graphs in Geometrically Embedded Neural Networks

Abstract

In this work we study a simplified model of a neural activity flow in networks, whose connectivity is based on geometrical embedding, rather than being lattices or fully connected graphs. We present numerical results showing that as the spectrum (set of eigenvalues of adjacency matrix) of the resulting activity-based network develops a scale-free dependency. Moreover it strengthens and becomes valid for a wider segment along with the simulation progress, which implies a highly organised structure of the analysed graph.