Abstract
BackgroundA central idea in biology is the hierarchical organization of cellular processes. A commonly used method to identify the hierarchical modular organization of network relies on detecting a global signature known as variation of clustering coefficient (so-called modularity scaling). Although several studies have suggested other possible origins of this signature, it is still widely used nowadays to identify hierarchical modularity, especially in the analysis of biological networks. Therefore, a further and systematical investigation of this signature for different types of biological networks is necessary.ResultsWe 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.ConclusionsHere 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.
Highlights
A central idea in biology is the hierarchical organization of cellular processes
To identify the hierarchical modularity of metabolic networks, Ravasz et al focused on detecting a “global signature” of network architecture [6,7]
They argued that this scaling law was not expected for a random scale-free network of similar sizes, indicating the absence of hierarchy in random networks. They used the B-A model to generate random scale-free networks [2]. One problem with their random network model, is that it does not take into account the existence of so-called super-hubs in metabolic networks (i.e. ATP and H2O)
Summary
A central idea in biology is the hierarchical organization of cellular processes. A commonly used method to identify the hierarchical modular organization of network relies on detecting a global signature known as variation of clustering coefficient (so-called modularity scaling). The high relevance between functional organization and topological features has motivated the development of statistical measures to characterize cellular networks 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 [1,2,3]. The number of nodes in the network is 5i This network model, which we explicitly denote by “deterministic hierarchical model”, has subsequently a great influence on the studies of network biology [8,9], and the scaling of C(k) is widely used to identify whether or not a network is hierarchically organized nowadays
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