Low-temperature behaviour of social and economic networks

Abstract

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 an ubiquitous property of real socio-economic networks, placing conditions on the diffusion of information across these systems.

References in corpus (23)

• The structure and function of complex networks
• Spatial Networks
• Hyperbolic Geometry of Complex Networks
• Global organization of metabolic fluxes in the bacterium, Escherichia coli
• The statistical mechanics of networks
• Small But Slow World: How Network Topology and Burstiness Slow Down Spreading
• Class of correlated random networks with hidden variables
• Fitness-dependent topological properties of the World Trade Web
• Clustering and information in correlation based financial networks
• The entropy of network ensembles
• The origin of degree correlations in the Internet and other networks
• Analytical maximum-likelihood method to detect patterns in real networks
• Reciprocity of weighted networks
• Generalized Bose-Fermi statistics and structural correlations in weighted networks
• Curvature and temperature of complex networks
• Network Transitivity and Matrix Models
• An ensemble approach to the analysis of weighted networks
• Multi-species grandcanonical models for networks with reciprocity
• Reconciling long-term cultural diversity and short-term collective social behavior
• Perturbing General Uncorrelated Networks
• Spatial effects in real networks: measures, null models, and applications
• The role of distances in the World Trade Web
• Network connection strengths: Another power-law?

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