Topological reinforcement as a principle of modularity emergence in brain networks

Modularity is a ubiquitous topological feature of structural brain networks at various scales. Although a variety of potential mechanisms have been proposed, the fundamental principles by which modularity emerges in neural networks remain elusive. We tackle this question with a plasticity model of neural networks derived from a purely topological perspective. Our topological reinforcement model acts enhancing the topological overlap between nodes, that is, iteratively allowing connections between non-neighbor nodes with high neighborhood similarity. This rule reliably evolves synthetic random networks toward a modular architecture. Such final modular structure reflects initial “proto-modules,” thus allowing to predict the modules of the evolved graph. Subsequently, we show that this topological selection principle might be biologically implemented as a Hebbian rule. Concretely, we explore a simple model of excitable dynamics, where the plasticity rule acts based on the functional connectivity (co-activations) between nodes. Results produced by the activity-based model are consistent with the ones from the purely topological rule in terms of the final network configuration and modules composition. Our findings suggest that the selective reinforcement of topological overlap may be a fundamental mechanism contributing to modularity emergence in brain networks. The self-organization of modular structure in brain networks is mechanistically poorly understood. We propose a simple plasticity model based on a fundamental principle, topological reinforcement, which promotes connections between nodes with high neighborhood similarity. Starting from a random network, this mechanism systematically promotes the emergence of modular architecture by enhancing initial weak proto-modules. Furthermore, we show that this topological selection principle can also be implemented in biological neural networks through a Hebbian plasticity rule, where what “fires together, wires together” and, under proper conditions, the results are consistent between both scenarios. We propose the topological reinforcement as a principle contributing to the emergence of modular structure in brain networks. This addresses the gap between previous pure generative and activity-based models of modularity emergence in brain networks, offering a common underlying principle at the topological level.