Origins of fractality in the growth of complex networks

By Chaoming Song, Shlomo Havlin, Hernán A. Makse. 2005

571 citations recorded by the source corpus.

Complex networks from such different fields as biology, technology or sociology share similar organization principles. The possibility of a unique growth mechanism promises to uncover universal origins of collective behaviour. In particular, the emergence of self-similarity in complex networks raises the fundamental question of the growth process according to which these structures evolve. Here we investigate the concept of renormalization as a mechanism for the growth of fractal and non-fractal modular networks. We show that the key principle that gives rise to the fractal architecture of networks is a strong effective ‘repulsion’ (or, disassortativity) between the most connected nodes (that is, the hubs) on all length scales, rendering them very dispersed. More importantly, we show that a robust network comprising functional modules, such as a cellular network, necessitates a fractal topology, suggestive of an evolutionary drive for their existence.

Subfields: Economics and Econometrics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/c6f1a3fec35503a488b43007bb12106a18f79e54

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Citations in the corpus

Complex network approaches to nonlinear time series analysis (2019, background): “In this respect,R or, more specifically, the scaling of the degree correlation determines the fractality of a VG [277], which is an interesting and potentially relevant property when studying fractal time series.”
Structure and Dynamics of Networks (2009, methodology): “A convenient, alternative representation of two-point correlations is given by the correlation function [Song et al., 2006]”
Self-similarity of complex networks (2005, background): “I Explore “self-similarity of complex networks” [21, 22] First work by Song et al.”
A small world of weak ties provides optimal global integration of self-similar modules in functional brain networks (2011, methodology): “Fractality can be determined from the study of the degreedegree correlation through the distribution, Pðk1;k2Þ to find a link between nodes with ðk1;k2Þ degree (22, 43).”
Statistical properties of visibility graph of energy dissipation rates in three-dimensional fully developed turbulence (2009, methodology): “]. In addition, some measures of anticorrelation, such as the Pearson coeﬃcient r, cannot capture the diﬀerence between a fractal and a non-fractalnetwork, sincer is not invariantunder renormalization[29, 34]. However, positive correlation of degrees using the Pearson coeﬃcient is suﬃcient to conﬁrm”
Random walks and diffusion on networks (2016, background): “he already added path of uedges and have a loose end. (If vis odd, one adds two paths of (v 1)=2 edges.) When u2, the (u;v)-tree model produces fractal and scalefree networks with = 1 + ln(u+ v)=ln2 [165, 167]. For such networks, the MFPT between hubs (which here too are dened as nodes that are pres”
Critical phenomena in complex networks (2007, unknown): “For description of these networks, see Song et al. (2005, 2006, 2007) and also Goh et al. (2006).”