The multiscale self-similarity of the weighted human brain connectome

Anatomical connectivity between different brain regions can be mapped to a network representation, the connectome, where the intensities of the links, the weights, influence resilience and functional processes. Yet, many features associated with these weights are not fully understood, particularly their multiscale organization. In this paper, we elucidate the architecture of weights, including weak ties, in multiscale human brain connectomes reconstructed from empirical data. Our findings reveal multiscale self-similarity, including the ordering of weak ties, in every individual connectome and group representative. This phenomenon is captured by a renormalization technique based on a geometric network model that replicates the observed structure of connectomes across all length scales, using the same connectivity law and weighting function for both weak and strong ties. The observed symmetry represents a signature of criticality in the weighted connectivity of the human brain and raises important questions for future research, such as the existence of symmetry breaking at some scale or whether it is preserved in cases of neurodegeneration or psychiatric disorder.Author summary: The human brain is a complex network where anatomical connections between regions, collectively known as the connectome, have varying intensities or weights. These weights influence brain resilience and functional processes, yet their organization across different length scales remains poorly understood. In this study, using human brain data, network geometry models, and a renormalization technique, we reveal that weighted connectomes resemble a fractal structure and exhibit multiscale self-similarity, meaning the same properties are observed at different resolutions. Weak and strong connections follow a consistent pattern and adhere to the same connectivity law across length scales. This multiscale self-similarity includes the organization of weak connections, which conform to the weak ties hypothesis in complex networks, asserting that weak ties are essential to their structure and function by facilitating integration and global information flow. In brain connectomes, we demonstrate that weak ties hold significant neurobiological importance, acting as essential bridges between distinct brain modules at each scale. Our findings not only enhance the understanding of the brain’s multiscale organization but also challenge existing theories that undervalue the role of weak ties in network connectivity, offering a framework to explore their significance in health and disease.