Networks -- used throughout the sciences in the study of biological, technological, and social complexity -- can often be too complex to visualize or understand.

In a May 1 Nature paper, “Hierarchical structure and the prediction of missing links in networks,” Santa Fe Institute (SFI) researchers Aaron Clauset, Cristopher Moore, and Mark Newman show that many real-world networks can be understood as a hierarchy of modules, where nodes cluster together to form modules, which themselves cluster into larger modules -- arrangements similar to the organization of sports players into teams, teams into conferences, and conferences into leagues, for example.

This hierarchical organization, the researchers show, can simultaneously explain a number of patterns previously discovered in networks, such as the surprising heterogeneity in the number of connections some nodes have, or the prevalence of triangles in a network diagram. Their discovery suggests that hierarchy may, in fact, be a fundamental organizational principle for complex networks.

Unlike much previous work in this area, Clauset, Moore, and Newman propose a direct but flexible model of hierarchical structure, which they apply to networks using the tools of statistical physics and machine learning.