Complex networks renormalisation: flows and fixed points

@misc{citeulike:2619766, abstract = {Complex networks in nature, society and technology share a set of topological features, reflecting some common organisational principles. Recently, it has been claimed that some complex networks are self-similar under a convenient renormalisation procedure. Here we present a general method to systematically study renormalisation flows in graphs. We find that the behaviour of some variables under renormalisation, such as the maximum and the average number of connections of a node, is described by simple scaling laws, characterised by critical exponents. This result holds for any class of graphs, from random to scale-free networks, from lattices to hierarchical graphs. Therefore, renormalisation flows for graphs display features similar to those found in the well-known renormalisation of spin systems. Critical exponents and scaling functions can be used to classify graphs in universality classes, and to uncover similarities between graph topologies that are inaccessible to a standard analysis.}, author = {Radicchi, Filippo and Ramasco, Jos\&\#xe9; J. and Barrat, Alain and Fortunato, Santo }, citeulike-article-id = {2619766}, eprint = {0803.3637}, keywords = {complex, networks}, month = {Mar}, posted-at = {2008-04-01 14:28:51}, priority = {2}, title = {Complex networks renormalisation: flows and fixed points}, url = {http://arxiv.org/abs/0803.3637}, year = {2008} }

TY - ELEC ID - citeulike:2619766 L3 - citeulike-article-id:2619766 TI - Complex networks renormalisation: flows and fixed points N2 - Complex networks in nature, society and technology share a set of topological features, reflecting some common organisational principles. Recently, it has been claimed that some complex networks are self-similar under a convenient renormalisation procedure. Here we present a general method to systematically study renormalisation flows in graphs. We find that the behaviour of some variables under renormalisation, such as the maximum and the average number of connections of a node, is described by simple scaling laws, characterised by critical exponents. This result holds for any class of graphs, from random to scale-free networks, from lattices to hierarchical graphs. Therefore, renormalisation flows for graphs display features similar to those found in the well-known renormalisation of spin systems. Critical exponents and scaling functions can be used to classify graphs in universality classes, and to uncover similarities between graph topologies that are inaccessible to a standard analysis. KW - complex KW - networks AU - Radicchi, Filippo AU - Ramasco, José AU - Barrat, Alain AU - Fortunato, Santo PY - 2008/Mar/25/ UR - http://arxiv.org/abs/0803.3637 ER -