Small-worldness favours network inference

TL;DR

This study investigates how small-world network properties influence the success of inferring neural network structures from time-series data, highlighting the roles of topological features like small-worldness and degree heterogeneity.

Contribution

It reveals that small-worldness facilitates network inference while degree heterogeneity impedes it, providing insights into neural network topology and inference challenges.

Findings

Small-world networks improve inference success rates.

Degree heterogeneity reduces inference accuracy.

C. elegans networks behave more like Erdös-Rényi models in inference performance.

Abstract

A main goal in the analysis of a complex system is to infer its underlying network structure from time-series observations of its behaviour. The inference process is often done by using bi-variate similarity measures, such as the cross-correlation (CC), however, the main factors favouring or hindering its success are still puzzling. Here, we use synthetic neuron models in order to reveal the main topological properties that frustrate or facilitate inferring the underlying network from CC measurements. Specifically, we use pulse-coupled Izhikevich neurons connected as in the Caenorhabditis elegans neural networks as well as in networks with similar randomness and small-worldness. We analyse the effectiveness and robustness of the inference process under different observations and collective dynamics, contrasting the results obtained from using membrane potentials and inter-spike interval time-series. We find that overall, small-worldness favours network inference and degree heterogeneity hinders it. In particular, success rates in C. elegans networks -- that combine small-world properties with degree heterogeneity -- are closer to success rates in Erd\"os-R\'enyi network models rather than those in Watts-Strogatz network models. These results are relevant to understand better the relationship between topological properties and function in different neural networks.