Hierarchical Organization of Modularity in Complex Networks

Abstract

Many real networks in nature and society share two generic properties: they are scale-free and they display a high degree of clustering. We show that the scale-free nature and high clustering of real networks are the consequence of a hierarchical organization, implying that small groups of nodes form increasingly large groups in a hierarchical manner, while maintaining a scale-free topology. In hierarchical networks the clustering coefficient follows a strict scaling law, which can be used to identify the presence of a hierarchical organization in real networks. We find that several real networks, such as the World Wide Web, actor network, the Internet at the domain level and the semantic web obey this scaling law, indicating that hierarchy is a fundamental characteristic of many complex systems. We the focus on the metabolic network of 43 distinct organisms and show that many small, highly connected topologic modules combine in a hierarchical manner into larger, less cohesive units, their number and degree of clustering following a power law. Within Escherichia Coli we find that the uncovered hierarchical modularity closely overlaps with known metabolic functions.