The Organization of Strong Links in Complex Networks

TL;DR

This paper uncovers a universal pattern of strong link organization in complex networks like brain, gene, social, and language systems, showing robustness and adaptive local learning rules that maintain efficiency.

Contribution

It introduces an integrative weight organization pattern for strong links and demonstrates its robustness and dynamic establishment through local learning rules.

Findings

Strong links occur between nodes with overlapping neighborhoods.

Small-world properties are robust to removal of weak links.

Local learning rules can dynamically establish this weight organization.

Abstract

A small-world topology characterizes many complex systems including the structural and functional organization of brain networks. The topology allows simultaneously for local and global efficiency in the interaction of the system constituents. However, it ignores the gradations of interactions commonly quantified by the link weight, w. Here, we identify an integrative weight organization for brain, gene, social, and language networks, in which strong links preferentially occur between nodes with overlapping neighbourhoods and the small-world properties are robust to removal of a large fraction of the weakest links. We also determine local learning rules that dynamically establish such weight organization in response to past activity and capacity demands, while preserving efficient local and global communication.