Emergence of Soft Communities from Geometric Preferential Attachment

Abstract

All real networks are different, but many have some structural properties in common. There seems to be no consensus on what the most common properties are, but scale-free degree distributions, strong clustering, and community structure are frequently mentioned without question. Surprisingly, there exists no simple generative mechanism explaining all the three properties at once in growing networks. Here we show how latent network geometry coupled with preferential attachment of nodes to this geometry fills this gap. We call this mechanism geometric preferential attachment (GPA), and validate it against the Internet. GPA gives rise to soft communities that provide a different perspective on the community structure in networks. The connections between GPA and cosmological models, including inflation, are also discussed.

arXiv comment10 pages, 6 figures

References in corpus (31)

• Emergence of scaling in random networks
• Community structure in social and biological networks
• Community detection in graphs
• Power-law distributions in empirical data
• Hierarchical organization of modularity in metabolic networks
• Functional cartography of complex metabolic networks
• Comparing community structure identification
• Hierarchical Organization in Complex Networks
• Evolution of the social network of scientific collaborations
• Clustering and preferential attachment in growing networks
• How Popular is Your Paper? An Empirical Study of the Citation Distribution
• Why social networks are different from other types of networks
• Structure of Growing Networks: Exact Solution of the Barabasi--Albert's Model
• Connectivity of Growing Random Networks
• Identity and Search in Social Networks
• Large-scale topological and dynamical properties of Internet
• Popularity versus Similarity in Growing Networks
• Measuring preferential attachment for evolving networks
• Growing networks with local rules: preferential attachment, clustering hierarchy and degree correlations
• Sustaining the Internet with Hyperbolic Mapping
• Highly clustered scale-free networks
• Subnetwork hierarchies of biochemical pathways
• Curvature of Co-Links Uncovers Hidden Thematic Layers in the World Wide Web
• Generic scale of the "scale-free" growing networks
• Triadic closure as a basic generating mechanism of communities in complex networks
• A Model for Social Networks
• Network Cosmology
• Majority Model on a network with communities
• Preferential attachment of communities: the same principle, but a higher level
• Coexistence of opposite opinions in a network with communities
• Emergence of Clustering in an Acquaintance Model without Homophily

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• Network Geometry Inference using Common Neighbors
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• Metric clusters in evolutionary games on scale-free networks
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• The exploration of the Adjacent Possible explains the emergence and evolution of social networks
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• Small worlds and clustering in spatial networks
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• Latent geometry of bipartite networks
• Embedding Graphs in Lorentzian Spacetime
• The inherent community structure of hyperbolic networks
• Gender and collaboration patterns in a temporal scientific authorship network
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• Scaling theory of fractal complex networks
• A geometry-induced topological phase transition in random graphs
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• Random hyperbolic graphs in $d+1$ dimensions
• Link persistence and conditional distances in multiplex networks
• Growing hyperbolic networks beyond two dimensions: the generalised popularity-similarity optimisation model
• Network Renormalization
• Optimisation of the coalescent hyperbolic embedding of complex networks
• Maximally modular structure of growing hyperbolic networks
• Zoo Guide to Network Embedding
• Growing homophilic networks are natural navigable small worlds
• Multi-layer network approach in modeling epidemics in an urban town
• Geometric evolution of complex networks
• Greedy routing optimisation in hyperbolic networks
• Navigability of Random Geometric Graphs in the Universe and Other Spacetimes
• Model-free hidden geometry of complex networks
• Geometric detection of hierarchical backbones in real networks
• Spatial Strength Centrality and the Effect of Spatial Embeddings on Network Architecture
• Geometric randomization of real networks with prescribed degree sequence
• Community detection in hypergraphs through hyperedge percolation
• Symmetry-driven embedding of networks in hyperbolic space
• Growing graphs with addition of communities
• Hidden multiscale organization and robustness of real multiplex networks
• Robustness and size-dependence of circadian rhythms in multiscale suprachiasmatic-nucleus networks