The success of complex networks at criticality

TL;DR

This paper introduces a metric to evaluate spike success in complex neural networks at criticality, revealing that scale-free small-world networks optimize spike success, unlike fully-connected networks.

Contribution

The study develops a new metric for spike success and demonstrates its effectiveness in analyzing neural dynamics across different network topologies.

Findings

Scale-free small-world networks have higher spike success.

Fully-connected networks show lower spike success.

Small-world property enhances spiking behavior in scale-free networks.

Abstract

In spiking neural networks an action potential could in principle trigger subsequent spikes in the neighbourhood of the initial neuron. A successful spike is that which trigger subsequent spikes giving rise to cascading behaviour within the system. In this study we introduce a metric to assess the success of spikes emitted by integrate-and-fire neurons arranged in complex topologies and whose collective behaviour is undergoing a phase transition that is identified by neuronal avalanches that become clusters of activation whose distribution of sizes can be approximated by a power-law. In numerical simulations we report that scale-free networks with the small-world property is the structure in which neurons possess more successful spikes. As well, we conclude both analytically and in numerical simulations that fully-connected networks are structures in which neurons perform worse. Additionally, we study how the small-world property affects spiking behaviour and its success in scale-free networks.