eprintid: 1106 rev_number: 13 eprint_status: archive userid: 6 dir: disk0/00/00/11/06 datestamp: 2012-02-01 16:07:06 lastmod: 2018-03-08 17:07:17 status_changed: 2012-02-01 16:07:06 type: article metadata_visibility: show creators_name: Garlaschelli, Diego creators_name: Ahnert, Sebastian E. creators_name: Fink, Thomas M.A. creators_name: Caldarelli, Guido creators_id: diego.garlaschelli@imtlucca.it creators_id: creators_id: creators_id: guido.caldarelli@imtlucca.it title: Temperature in complex networks ispublished: submitted subjects: HA subjects: QC divisions: EIC full_text_status: public keywords: Disordered Systems and Neural Networks (cond-mat.dis-nn); Statistical Mechanics (cond-mat.stat-mech); Adaptation and Self-Organizing Systems (nlin.AO); Physics and Society (physics.soc-ph) abstract: Various statistical-mechanics approaches to complex networks have been proposed to describe expected topological properties in terms of ensemble averages. Here we extend this formalism by introducing the fundamental concept of graph temperature, controlling the degree of topological optimization of a network. We recover the temperature-dependent version of various important models as particular cases of our approach, and show examples where, remarkably, the onset of a percolation transition, a scale-free degree distribution, correlations and clustering can be understood as natural properties of an optimized (low-temperature) topology. We then apply our formalism to real weighted networks and we compute their temperature, finding that various techniques used to extract information from complex networks are again particular cases of our approach. date: 2006 date_type: submitted publication: Physical Review E publisher: American Physical Society refereed: FALSE issn: 1539-3755 official_url: http://arxiv.org/abs/cond-mat/0606805 citation: Garlaschelli, Diego and Ahnert, Sebastian E. and Fink, Thomas M.A. and Caldarelli, Guido Temperature in complex networks. Physical Review E. ISSN 1539-3755 (Submitted) (2006) document_url: http://eprints.imtlucca.it/1106/1/Garlaschelli_Ahnert_Fink_Caldarelli.pdf