Characterization and modeling of weighted networks

By Marc Barthelemy, Alain Barrat, Romualdo Pastor-Satorras, Alessandro Vespignani. 2004

349 citations recorded by the source corpus.

We review the main tools which allow for the statistical characterization of weighted networks. We then present two case studies, the airline connection network and the scientific collaboration network which are representatives of critical infrastructure and social system, respectively. The main empirical results are (i) the broad distributions of various quantities and (ii) the existence of weight-topology correlations. These measurements show that weights are relevant and that in general the modeling of complex networks must go beyond topology. We review a model which provides an explanation for the features observed in several real-world networks. This model of weighted network formation relies on the dynamical coupling between topology and weights, considering the rearrangement of new links are introduced in the system.

Subfields: Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/78a12cba77449cc7e8aff1f0142839ca8a862f66

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In Geometry and Topology

In Statistical and Nonlinear Physics

Citations in the corpus

Social network analysis of animal behaviour : a promising tool for the study of sociality (2008, background): “A related idea in a weighted network is relationship strength, which is the weight of the tie (Barthélemy et al. 2005).”
Characterization of complex networks: A survey of measurements (2005, methodology): “ut i . For weighted networks, the deﬁnitions of degree given above can be used, but a quantity called strength of i, si, deﬁned as the sum of the weights of the corresponding links, is generally used [24]: sout i = X j wij (1) sin i = X j wji (2) Table 1 lists the basic symbols used in the paper. 3 ”
The evolution of the world trade web: a weighted-network analysis (2010, background): “Second, one might assess how much the partners of a node are themselves characterized by a high strength by computing either the weighted average of nearest-neighbor node degrees (WANND, see Barth´elemy et al., 2005) or the arithmetic average of nearest-neighbor strengths (ANNS).”
Social cohesion in a hierarchically structured embayment population of Indo-Pacific bottlenose dolphins (2009, background): “These included the strength, which is a measure of gregariousness and is the sum of the association indices for each individual (Barthélemy et al. 2005), the clustering coefficient,”
The application of graph theoretical analysis to complex networks in the brain. (2007, positive): “Most graph measures have only been defined for the simplest case of unweighted graph, but in many cases weighted graphs are more accurate models of real networks (Latora and Marchiori, 2001, 2003; Newman, 2004; Barrat et al., 2004; Park et al., 2004; Barthelemy et al., 2005; Onnela et al., 2005).”
Topological properties of stock market networks: The case of Brazil (2010, background): “One of the important networkmeasures that we studied is defined as disparity [22].”
Vital nodes identification in complex networks (2016, background): “When the weights are independent from the topology, we have s ≃ 〈w〉k where 〈w〉 is the average weight [275].”
Exploring the structure of the U.S. intercity passenger air transportation network: a weighted complex network approach (2008, background): “On the other hand, a network with C^kC will have many interconnected triplets generated by edges with low weights, and the high weight edges do not form the interconnected triplets (Barrât et al. 2004a; Bathelemy et al. 2005; Costa et al. 2007; Park et al. 2004).”
Graph theoretical analysis of complex networks in the brain (2007, background): “Several authors have discussed the analysis of weighted graphs [ 41-47 ].”