Revisiting the variation of clustering coefficient of biological networks suggests new modular structure

We analyzed a variety of biological networks and found that the commonly used signature of hierarchical modularity is actually the reflection of spoke-like topology, suggesting a different view of network architecture. We proved that the existence of super-hubs is the origin that the clustering coefficient of a node follows a particular scaling law with degree k in metabolic networks. To study the modularity of biological networks, we systematically investigated the relationship between repulsion of hubs and variation of clustering coefficient. We provided direct evidences for repulsion between hubs being the underlying origin of the variation of clustering coefficient, and found that for biological networks having no anti-correlation between hubs, such as gene co-expression network, the clustering coefficient doesn’t show dependence of degree.Here we have shown that the variation of clustering coefficient is neither sufficient nor exclusive for a network to be hierarchical. Our results suggest the existence of spoke-like modules as opposed to “deterministic model” of hierarchical modularity, and suggest the need to reconsider the organizational principle of biological hierarchy.The high relevance between functional organization and topological features has motivated the development of statistical measures to characterize cellular networks. Increasingly, these measures reveal that biological network organization is characterized by the power law of degree distribution, the concept of modularity and the degree correlations on connected nodes [1-3]. Networks with high modularity have dense connections between the nodes within same cellular functions but sparse connections between nodes in different functions. Furthermore, a central theory in biology is the hierarchical organization of cellular processes, which means that high-level processes are build by connecting low-level ones [4,5]. For example, the process mitosis is composed by several low-level functions, such