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.
Highlights
Complex networks have attracted the interest of physicists, because statistical physics has proven to be an effective tool for the measurement and explanation of robust empirical properties of these networks [1,2]
We have introduced the concept of “graph temperature”, which can vary from zero to infinity, in order to explore the behaviour of networks in the limit of large network size, while keeping the local properties well-defined
Since our methodology makes use of statistical graph ensembles that extend the class of Exponential Random Graphs widely used in social network analysis, it has a natural application as a generalized model of social and economic networks
Summary
Complex networks have attracted the interest of physicists, because statistical physics has proven to be an effective tool for the measurement and explanation of robust empirical properties of these networks [1,2]. In particular, often exhibit particular topological properties, such as the presence of a giant connected component (a set of mutually reachable vertices spanning a finite fraction of the system), the “small-world” property (the combination of a large density of triangles and a short distance among nodes), community structure (a subdivision of the network into modules of densely interconnected nodes) and a broad-degree distribution (the presence of many more highly connected vertices than expected in random graphs). We show that, if the analogy with statistical physics is completed via the introduction of the concept of graph temperature, all the above empirical properties can be understood as the consequences of a single phenomenon: the fact that real networks tend to have a low value of the temperature, presumably as the result of a topological optimization driven by the cost of establishing links. Structure, can be understood in terms of the low-temperature behaviour of real networks
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
