Correlations in weighted networks

Abstract

We develop a statistical theory to characterize correlations in weighted networks. We define the appropriate metrics quantifying correlations and show that strictly uncorrelated weighted networks do not exist due to the presence of structural constraints. We also introduce an algorithm for generating maximally random weighted networks with arbitrary $P(k,s)$ to be used as null models. The application of our measures to real networks reveals the importance of weights in a correct understanding and modeling of these heterogeneous systems.

4 pages, 2 figures

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• Reciprocity of weighted networks
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• Robustness of onion-like correlated networks against targeted attacks
• Enhanced reconstruction of weighted networks from strengths and degrees
• Directed clustering in weighted networks: a new perspective
• The hidden geometry of weighted complex networks
• On the rich-club effect in dense and weighted networks
• A Unifying Framework for Measuring Weighted Rich Clubs
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• Reconstructing the world trade multiplex: the role of intensive and extensive biases
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• The Organization of Strong Links in Complex Networks
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• Robustness of cooperation on scale-free networks under continuous topological change
• Statistical Mechanics of Multi-Edge Networks
• Spatio-Temporal Patterns of the International Merger and Acquisition Network
• A general formulation of long-range degree correlations in complex networks
• Assortative Mixing in Weighted Directed Networks
• The role of adjacency matrix degeneration in maximum entropy weighted network models
• Network Renormalization
• The Network Picture of Labor Flow
• The configuration multi-edge model: Assessing the effect of fixing node strengths on weighted network magnitudes
• Complex Networks: Time-Dependent Connections and Silent Nodes
• Geometric randomization of real networks with prescribed degree sequence
• Quantitative modeling of degree-degree correlation in complex networks
• WEM: A Node Importance Algorithm in Weighted Networks
• Approximate Conditional Sampling for Pattern Detection in Weighted Networks
• Nonequilibrium Thermodynamics in Measuring Carbon Footprints: Disentangling Structure and Artifact in Input-Output Accounting
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