IMT Institutional Repository: No conditions. Results ordered -Date Deposited. 2020-02-25T06:15:36ZEPrintshttp://eprints.imtlucca.it/images/logowhite.pnghttp://eprints.imtlucca.it/2015-12-03T15:37:21Z2018-03-08T17:02:20Zhttp://eprints.imtlucca.it/id/eprint/2966This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/29662015-12-03T15:37:21ZOptimal Scales in Weighted NetworksThe analysis of networks characterized by links with heterogeneous intensity or weight suffers from two long-standing problems of arbitrariness. On one hand, the definitions of topological properties introduced for binary graphs can be generalized in non-unique ways to weighted networks. On the other hand, even when a definition is given, there is no natural choice of the (optimal) scale of link intensities (e.g. the money unit in economic networks). Here we show that these two seemingly independent problems can be regarded as intimately related, and propose a common solution to both. Using a formalism that we recently proposed in order to map a weighted network to an ensemble of binary graphs, we introduce an information-theoretic approach leading to the least biased generalization of binary properties to weighted networks, and at the same time fixing the optimal scale of link intensities. We illustrate our method on various social and economic networks.Diego Garlaschellidiego.garlaschelli@imtlucca.itSebastian E. AhnertThomas M.A. FinkGuido Caldarelliguido.caldarelli@imtlucca.it2014-06-16T11:23:49Z2018-03-08T17:01:43Zhttp://eprints.imtlucca.it/id/eprint/2201This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/22012014-06-16T11:23:49ZLow-Temperature behaviour of social and economic networksReal-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. Diego Garlaschellidiego.garlaschelli@imtlucca.itSebastian E. AhnertThomas M.A. FinkGuido Caldarelliguido.caldarelli@imtlucca.it2012-02-01T16:07:06Z2018-03-08T17:07:17Zhttp://eprints.imtlucca.it/id/eprint/1106This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/11062012-02-01T16:07:06ZTemperature in complex networksVarious 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. Diego Garlaschellidiego.garlaschelli@imtlucca.itSebastian E. AhnertThomas M.A. FinkGuido Caldarelliguido.caldarelli@imtlucca.it2012-02-01T15:39:59Z2018-03-08T17:09:14Zhttp://eprints.imtlucca.it/id/eprint/1104This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/11042012-02-01T15:39:59ZEnsemble approach to the analysis of weighted networksWe present an approach to the analysis of weighted networks, by providing a straightforward generalization of any network measure defined on unweighted networks, such as the average degree of the nearest neighbors, the clustering coefficient, the “betweenness,” the distance between two nodes, and the diameter of a network. All these measures are well established for unweighted networks but have hitherto proven difficult to define for weighted networks. Our approach is based on the translation of a weighted network into an ensemble of edges. Further introducing this approach we demonstrate its advantages by applying the clustering coefficient constructed in this way to two real-world weighted networks.Sebastian E. AhnertDiego Garlaschellidiego.garlaschelli@imtlucca.itThomas M.A. FinkGuido Caldarelliguido.caldarelli@imtlucca.it2012-02-01T11:33:12Z2018-03-08T17:05:45Zhttp://eprints.imtlucca.it/id/eprint/1094This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/10942012-02-01T11:33:12ZApplying weighted network measures to microarray distance matricesIn recent work we presented a new approach to the analysis of weighted networks, by providing a straightforward generalization of any network measure defined on unweighted networks. This approach is based on the translation of a weighted network into an ensemble of edges, and is particularly suited to the analysis of fully connected weighted networks. Here we apply our method to several such networks including distance matrices, and show that the clustering coefficient, constructed by using the ensemble approach, provides meaningful insights into the systems studied. In the particular case of two datasets from microarray experiments the clustering coefficient identifies a number of biologically significant genes, outperforming existing identification approaches.Sebastian E. AhnertDiego Garlaschellidiego.garlaschelli@imtlucca.itThomas M.A. FinkGuido Caldarelliguido.caldarelli@imtlucca.it