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 (28)

• Spatial Networks
• Graph Embedding Techniques, Applications, and Performance: A Survey
• The worldwide air transportation network: Anomalous centrality, community structure, and cities' global roles
• Hyperbolic Geometry of Complex Networks
• The statistical mechanics of networks
• The phase transition in inhomogeneous random graphs
• Is the Boston subway a small-world network ?
• Random Geometric Graphs
• Class of correlated random networks with hidden variables
• Self-similarity of complex networks and hidden metric spaces
• Cut-offs and finite size effects in scale-free networks
• Equivalence and nonequivalence of ensembles: Thermodynamic, macrostate, and measure levels
• Consistency under sampling of exponential random graph models
• Multiscale unfolding of real networks by geometric renormalization
• Random geometric graphs with general connection functions
• Emergence of Soft Communities from Geometric Preferential Attachment
• A nonuniform popularity-similarity optimization (nPSO) model to efficiently generate realistic complex networks with communities
• Structural properties of spatially embedded networks
• Clustering implies geometry in networks
• Connectivity of soft random geometric graphs
• Exact Solution of Ising Model on a Small-World Network
• Explosion in weighted Hyperbolic Random Graphs and Geometric Inhomogeneous Random Graphs
• Soft communities in similarity space
• Sparse Maximum-Entropy Random Graphs with a Given Power-Law Degree Distribution
• Nonequilibrium phase transitions in systems with long-range interactions
• Entropy of Spatial Network Ensembles
• Sharp asymptotic for the chemical distance in long-range percolation
• Duality between equilibrium and growing networks

Cited by in corpus (18)

• Network Geometry
• Geometric renormalization unravels self-similarity of the multiscale human connectome
• Detecting the ultra low dimensionality of real networks
• Emergence of geometric Turing patterns in complex networks
• Structural measures of similarity and complementarity in complex networks
• A geometry-induced topological phase transition in random graphs
• Random hyperbolic graphs in $d+1$ dimensions
• Weighted hypersoft configuration model
• Network Renormalization
• Spatial Strength Centrality and the Effect of Spatial Embeddings on Network Architecture
• Geometric detection of hierarchical backbones in real networks
• Strength and weakness of disease-induced herd immunity in networks
• 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