The hidden geometry of weighted complex networks

Abstract

The topology of many real complex networks has been conjectured to be embedded in hidden metric spaces, where distances between nodes encode their likelihood of being connected. Besides of providing a natural geometrical interpretation of their complex topologies, this hypothesis yields the recipe for sustainable Internet's routing protocols, sheds light on the hierarchical organization of biochemical pathways in cells, and allows for a rich characterization of the evolution of international trade. We present empirical evidence that this geometric interpretation also applies to the weighted organisation of real complex networks. We introduce a very general and versatile model and use it to quantify the level of coupling between their topology, their weights, and an underlying metric space. Our model accurately reproduces both their topology and their weights, and our results suggest that the formation of connections and the assignment of their magnitude are ruled by different processes.

Major revisions since the previous version. 9 pages, 4 figures (Supplementary: 33 pages, 41 figures)

References in corpus (14)

• Hyperbolic Geometry of Complex Networks
• Extracting the multiscale backbone of complex weighted networks
• Navigability of Complex Networks
• Sustaining the Internet with Hyperbolic Mapping
• Self-similarity of complex networks and hidden metric spaces
• Emergence of communities in weighted networks
• Quantifying randomness in real networks
• Generalized Bose-Fermi statistics and structural correlations in weighted networks
• Correlations in weighted networks
• Network Geometry Inference using Common Neighbors
• Rich-club vs rich-multipolarization phenomena in weighted networks
• Navigating ultrasmall worlds in ultrashort time
• The role of adjacency matrix degeneration in maximum entropy weighted network models
• On the diameter of hyperbolic random graphs

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• Geometric explanation of the rich-club phenomenon in complex networks
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• A geometry-induced topological phase transition in random graphs
• Weighted hypersoft configuration model
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• The multiscale self-similarity of the weighted human brain connectome
• Community detection in hypergraphs through hyperedge percolation
• High Performance Algorithms for Quantum Gravity and Cosmology
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• Random walk with hyperbolic probabilities
• Abrupt efficiency collapse in real-world complex weighted networks: robustness decrease with link weights heterogeneity
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