Structure of cycles and local ordering in complex networks |
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Authors: | G Caldarelli R Pastor-Satorras A Vespignani |
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Institution: | (1) INFM UdR Roma 1, Dipartimento di Fisica, Universitá La Sapienza , P.le A. Moro 2, 00185 Roma, Italy;(2) Departament de Física i Enginyeria Nuclear, Universitat Politécnica de Catalunya, Campus Nord, 08034 Barcelona, Spain;(3) Laboratoire de Physique Théorique (UMR du CNRS 8627), Bâtiment 210, Université de Paris-Sud, 91405 Orsay Cedex, France |
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Abstract: | We study the properties of quantities aimed at the characterization of grid-like ordering in complex networks. These quantities are based on the global and local behavior of cycles of order four, which are the minimal structures able to identify rectangular clustering. The analysis of data from real networks reveals the ubiquitous presence of a statistically high level of grid-like ordering that is non-trivially correlated with the local degree properties. These observations provide new insights on the hierarchical structure of complex networks.Received: 6 November 2003, Published online: 17 February 2004PACS:
89.75.-k Complex systems - 89.75.Fb Structures and organization in complex systems |
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