Robustness of functional networks at criticality against structural defects

TL;DR

This study investigates how the functional network properties of a critical 2D Ising model are resilient to structural damage, revealing robustness of scale-free and small-world features under significant lesions.

Contribution

It demonstrates that functional networks at criticality maintain scale-free and small-world properties despite extensive structural defects, using a 2D Ising model as a conceptual framework.

Findings

Functional networks remain scale-free and small-world despite structural defects.

Robustness persists below the percolation threshold.

Insights into neuronal network resilience from statistical mechanics models.

Abstract

The robustness of dynamical properties of neuronal networks against structural damages is a central problem in computational and experimental neuroscience. Research has shown that the cortical network of a healthy brain works near a critical state, and moreover, that functional neuronal networks often have scale-free and small-world properties. In this work, we study how the robustness of simple functional networks at criticality is affected by structural defects. In particular, we consider a 2D Ising model at the critical temperature and investigate how its functional network changes with the increasing degree of structural defects. We show that the scale-free and small-world properties of the functional network at criticality are robust against large degrees of structural lesions while the system remains below the percolation limit. Although the Ising model is only a conceptual description of a two-state neuron, our research reveals fundamental robustness properties of functional networks derived from classical statistical mechanics models.