The effects of spatial constraints on the evolution of weighted complex networks

Abstract

Motivated by the empirical analysis of the air transportation system, we define a network model that includes geographical attributes along with topological and weight (traffic) properties. The introduction of geographical attributes is made by constraining the network in real space. Interestingly, the inclusion of geometrical features induces non-trivial correlations between the weights, the connectivity pattern and the actual spatial distances of vertices. The model also recovers the emergence of anomalous fluctuations in the betweenness-degree correlation function as first observed by Guimerà and Amaral [Eur. Phys. J. B {\bf 38}, 381 (2004)]. The presented results suggest that the interplay between weight dynamics and spatial constraints is a key ingredient in order to understand the formation of real-world weighted networks.

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• Modelling the Air Transport with Complex Networks: a short review
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• The International Trade Network: weighted network analysis and modelling
• Microdynamics in stationary complex networks
• Robustness of Trans-European Gas Networks
• Optimal Traffic Networks
• Vulnerability of weighted networks
• Latent Space Models for Dynamic Networks with Weighted Edges
• Multi-scale analysis of the European airspace using network community detection
• Stochasticity in pandemic spread over the World Airline Network explained by local flight connections
• Centrality anomalies in complex networks as a result of model over-simplification
• Geometric origin of scaling in large traffic networks
• Effects of accelerating growth on the evolution of weighted complex networks
• Spatial correlations in attribute communities
• A growth model for water distribution networks with loops
• Determinant representations of scalar products for the open XXZ chain with non-diagonal boundary terms
• Complex Networks: Time-Dependent Connections and Silent Nodes
• A Latent Parameter Node-Centric Model for Spatial Networks
• Random walk models for the propagation of signalling molecules in one-dimensional spatial networks and their continuum limit
• Spatial Strength Centrality and the Effect of Spatial Embeddings on Network Architecture
• Solvable Metric Growing Networks
• Analytic Solution to Clustering Coefficients on Weighted Networks