Small worlds and clustering in spatial networks

Abstract

Networks with underlying metric spaces attract increasing research attention in network science, statistical physics, applied mathematics, computer science, sociology, and other fields. This attention is further amplified by the current surge of activity in graph embedding. In the vast realm of spatial network models, only a few reproduce even the most basic properties of real-world networks. Here, we focus on three such properties--sparsity, small worldness, and clustering--and identify the general subclass of spatial homogeneous and heterogeneous network models that are sparse small worlds and that have nonzero clustering in the thermodynamic limit. We rely on the maximum entropy approach where network links correspond to noninteracting fermions whose energy dependence on spatial distances determines network small worldness and clustering.

References in corpus (6)

• Hyperbolic Geometry of Complex Networks
• Self-similarity of complex networks and hidden metric spaces
• Equivalence and nonequivalence of ensembles: Thermodynamic, macrostate, and measure levels
• Emergence of Soft Communities from Geometric Preferential Attachment
• Structural properties of spatially embedded networks
• Exact Solution of Ising Model on a Small-World Network

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• Spatial Strength Centrality and the Effect of Spatial Embeddings on Network Architecture
• Geometric detection of hierarchical backbones in real networks
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• Community detection in hypergraphs through hyperedge percolation
• Dynamics of hot random hyperbolic graphs
• Random Apollonian networks with tailored clustering coefficient
• Symmetry-driven embedding of networks in hyperbolic space
• Dynamics of cold random hyperbolic graphs with link persistence
• On the distances within cliques in a soft random geometric graph