2003/11/18 by Alain Barrat, Marc Barthélemy, Marc Barthelemy +3 · 3 citations
Computer Science · Physics and Astronomy · #Complex Network Analysis Techniques #Opinion Dynamics and Social Influence #Topological and Geometric Data Analysis #cond-mat.stat-mech
paper · pdf · doi:10.1073/pnas.0400087101
published as Proc. Natl. Acad. Sci. USA 101, 3747 (2004)
arxiv created 2003/11/18 · openalex publication_date 2004/03/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/03
Networked structures arise in a wide array of different contexts such as technological and transportation infrastructures, social phenomena, and biological systems. These highly interconnected systems have recently been the focus of a great deal of attention that has uncovered and characterized their topological complexity. Along with a complex topological structure, real networks display a large heterogeneity in the capacity and intensity of the connections. These features, however, have mainly not been considered in past studies where links are usually represented as binary states, i.e., either present or absent. Here, we study the scientific collaboration network and the world-wide air-transportation network, which are representative examples of social and large infrastructure systems, respectively. In both cases it is possible to assign to each edge of the graph a weight proportional to the intensity or capacity of the connections among the various elements of the network. We define appropriate metrics combining weighted and topological observables that enable us to characterize the complex statistical properties and heterogeneity of the actual strength of edges and vertices. This information allows us to investigate the correlations among weighted quantities and the underlying topological structure of the network. These results provide a better description of the hierarchies and organizational principles at the basis of the architecture of weighted networks.