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Entropy 2013, 15(8), 3148-3169;

Low-Temperature Behaviour of Social and Economic Networks

Lorentz Institute of Theoretical Physics, University of Leiden, Niels Bohrweg 2, Leiden 2333 CA, The Netherlands
Theory of Condensed Matter, Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, Cambridge CB3 0HE, UK
London Institute for Mathematical Sciences, 22 South Audley St, London W1K 2NY, UK
IMT Alti Studi Lucca, Piazza S. Ponziano 6, Lucca 55100, Italy
ISC-CNR, Dipartimento di Fisica, Università La Sapienza, P.le A. Moro 2, Roma 00185, Italy
Author to whom correspondence should be addressed.
Received: 19 June 2013 / Revised: 17 July 2013 / Accepted: 30 July 2013 / Published: 5 August 2013
(This article belongs to the Special Issue Social Networks and Information Diffusion)
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Real-world social and economic networks typically display a number of particular topological properties, such as a giant connected component, a broad degree distribution, the small-world property and the presence of communities of densely interconnected nodes. Several models, including ensembles of networks, also known in social science as Exponential Random Graphs, have been proposed with the aim of reproducing each of these properties in isolation. Here, we define a generalized ensemble of graphs by introducing the concept of graph temperature, controlling the degree of topological optimization of a network. We consider the temperature-dependent version of both existing and novel models and show that all the aforementioned topological properties can be simultaneously understood as the natural outcomes of an optimized, low-temperature topology. We also show that seemingly different graph models, as well as techniques used to extract information from real networks are all found to be particular low-temperature cases of the same generalized formalism. One such technique allows us to extend our approach to real weighted networks. Our results suggest that a low graph temperature might be a ubiquitous property of real socio-economic networks, placing conditions on the diffusion of information across these systems.
Keywords: complex networks; graph ensembles; graph temperature complex networks; graph ensembles; graph temperature
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Garlaschelli, D.; Ahnert, S.E.; Fink, T.M.A.; Caldarelli, G. Low-Temperature Behaviour of Social and Economic Networks. Entropy 2013, 15, 3148-3169.

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