Renormalization flows in complex networks

Abstract

Complex networks have acquired a great popularity in recent years, since the graph representation of many natural, social and technological systems is often very helpful to characterize and model their phenomenology. Additionally, the mathematical tools of statistical physics have proven to be particularly suitable for studying and understanding complex networks. Nevertheless, an important obstacle to this theoretical approach is still represented by the difficulties to draw parallelisms between network science and more traditional aspects of statistical physics. In this paper, we explore the relation between complex networks and a well known topic of statistical physics: renormalization. A general method to analyze renormalization flows of complex networks is introduced. The method can be applied to study any suitable renormalization transformation. Finite-size scaling can be performed on computer-generated networks in order to classify them in universality classes. We also present applications of the method on real networks.

12 pages, 11 figures

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• Weighted Fractal Networks
• Dynamics and Processing in Finite Self-Similar Networks
• Random elastic networks : strong disorder renormalization approach
• Irreversible Aggregation and Network Renormalization
• Random Sequential Renormalization of Networks I: Application to Critical Trees
• Agglomerative Percolation on Bipartite Networks: A Novel Type of Spontaneous Symmetry Breaking
• Network Renormalization
• Finite-size scaling of geometric renormalization flows in complex networks
• Random Sequential Renormalization and Agglomerative Percolation in Networks: Application to Erd"os-R'enyi and Scale-free Graphs
• Laplacian Renormalization Group: An introduction to heterogeneous coarse-graining
• Scaling properties of scale-free networks in degree-thresholding renormalization flows
• Inhomogeneous random graphs with infinite-mean fitness variables