Synopsis: Zooming out on complex networks

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Complex Networks Renormalization: Flows and Fixed Points

Filippo Radicchi, José J. Ramasco, Alain Barrat, and Santo Fortunato

Published October 1, 2008

Complex networks appear in extremely diverse contexts, such as telecommunications, protein interactions, and social interactions. Yet many of these networks appear to share certain nontrivial, similar patterns of connection between their elements. Understanding the origins of these patterns and identifying and characterizing new ones is one of the main driving forces for research in complex networks. An interesting and open question pertinent to this effort is how the structural organization of a network evolves as it is observed on increasingly larger scales—from individual nodes to the network as a whole.

Building on several contributions to this problem [1,2], Filippo Radicchi, José Ramasco, and Santo Fortunato at the ISI Foundation in Torino and Alain Barrat at Université Paris-Sud take another significant step forward in a paper appearing in Physical Review Letters. Drawing from statistical mechanics, they use well-established real-space renormalization and finite-size scaling techniques and formulate a systematic approach that analyzes the evolution (or “flow”) of two judiciously chosen variables that characterize the structure of the network as they increase the scale of observation. They apply this approach to a number of artificial networks (or graphs), some of which are models of real networks, and find universal behavior that has not been identified before.

Will this approach lead to a full classification of complex networks into universality classes? That remains to be seen. But the work from Radicci et al. already complements the existing characterization of topology of complex networks. – Ling Miao

[1] C. Song, S. Havlin, and H. A. Makse, Nature 433, 392 (2005); Nature Phys. 2, 275 (2006).

[2] K.-I. Goh, G. Salvi, B. Kahng, and D. Kim, Phys. Rev. Lett. 96, 018701 (2006).

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