Self-similarity of complex networks and hidden metric spaces

@misc{citeulike:2197822, abstract = {We demonstrate that the self-similarity of some scale-free networks with respect to a simple degree-thresholding renormalization scheme finds a natural interpretation in the assumption that network nodes exist in hidden metric spaces. Clustering, i.e., cycles of length three, plays a crucial role in this framework as a topological reflection of the triangle inequality in the hidden geometry. We prove that a class of hidden variable models with underlying metric spaces are able to accurately reproduce the self-similarity properties that we measured in the real networks. Our findings indicate that hidden geometries underlying these real networks are a plausible explanation for their observed topologies and, in particular, for their self-similarity with respect to the degree-based renormalization.}, author = {Serrano, Angeles M. and Krioukov, Dmitri and Boguna, Marian }, citeulike-article-id = {2197822}, eprint = {0710.2092}, keywords = {complex, metrics, networks, self-similarity}, month = {Oct}, posted-at = {2008-03-14 05:45:38}, priority = {2}, title = {Self-similarity of complex networks and hidden metric spaces}, url = {http://arxiv.org/abs/0710.2092}, year = {2007} }

TY - ELEC ID - citeulike:2197822 L3 - citeulike-article-id:2197822 TI - Self-similarity of complex networks and hidden metric spaces N2 - We demonstrate that the self-similarity of some scale-free networks with respect to a simple degree-thresholding renormalization scheme finds a natural interpretation in the assumption that network nodes exist in hidden metric spaces. Clustering, i.e., cycles of length three, plays a crucial role in this framework as a topological reflection of the triangle inequality in the hidden geometry. We prove that a class of hidden variable models with underlying metric spaces are able to accurately reproduce the self-similarity properties that we measured in the real networks. Our findings indicate that hidden geometries underlying these real networks are a plausible explanation for their observed topologies and, in particular, for their self-similarity with respect to the degree-based renormalization. KW - complex KW - metrics KW - networks KW - self-similarity AU - Serrano, Angeles AU - Krioukov, Dmitri AU - Boguna, Marian PY - 2007/Oct/10/ UR - http://arxiv.org/abs/0710.2092 ER -