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Classes of complex networks defined by role-to-role connectivity profiles


In physical, biological, technological and social systems, interactions between units give rise to intricate networks. These—typically non-trivial—structures, in turn, critically affect the dynamics and properties of the system. The focus of most current research on complex networks is, still, on global network properties. A caveat of this approach is that the relevance of global properties hinges on the premise that networks are homogeneous, whereas most real-world networks have a markedly modular structure. Here, we report that networks with different functions, including the Internet, metabolic, air transportation and protein interaction networks, have distinct patterns of connections among nodes with different roles, and that, as a consequence, complex networks can be classified into two distinct functional classes on the basis of their link type frequency. Importantly, we demonstrate that these structural features cannot be captured by means of often studied global properties.

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Figure 1: Modularity and degree distribution explain most degree–degree correlations in complex networks.
Figure 2: Role-to-role connectivity patterns.
Figure 3: Modules and role-to-role connectivity signatures in different network types.


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We thank R. D. Malmgren, E. N. Sawardecker, S. M. D. Seaver, D. B. Stouffer and M. J. Stringer for useful comments and suggestions. R.G. and M.S.-P. thank the Fulbright Program. L.A.N.A. gratefully acknowledges the support of a NIH/NIGMS K-25 award, of NSF award SBE 0624318, of the J. S. McDonnell Foundation and of the W. M. Keck Foundation.

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Correspondence to Roger Guimerà or Luís A. N. Amaral.

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Guimerà, R., Sales-Pardo, M. & Amaral, L. Classes of complex networks defined by role-to-role connectivity profiles. Nature Phys 3, 63–69 (2007).

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