Random graphs and real networks with weak geometric coupling

Abstract

Geometry can be used to explain many properties commonly observed in real networks. It is therefore often assumed that real networks, especially those with high average local clustering, live in an underlying hidden geometric space. However, it has been shown that finite size effects can also induce substantial clustering, even when the coupling to this space is weak or non existent. In this paper, we study the weakly geometric regime, where clustering is absent in the thermodynamic limit but present in finite systems. Extending Mercator, a network embedding tool based on the Popularity$\times$Similarity ${\mathbb{S}}^1$/${\mathbb{H}}^2$ static geometric network model, we show that, even when the coupling to the geometric space is weak, geometric information can be recovered from the connectivity alone. The fact that several real networks are best described in this quasi-geometric regime suggests that the transition between non-geometric and geometric networks is not a sharp one.

arXiv comment11 pages, 5 figures, 1 table

References in corpus (31)

• Statistical mechanics of complex networks
• The structure and function of complex networks
• Graph Embedding Techniques, Applications, and Performance: A Survey
• Hyperbolic Geometry of Complex Networks
• Modularity from Fluctuations in Random Graphs and Complex Networks
• Random Walks on Multiplex Networks
• Navigability of Complex Networks
• Sustaining the Internet with Hyperbolic Mapping
• MuxViz: A Tool for Multilayer Analysis and Visualization of Networks
• Self-similarity of complex networks and hidden metric spaces
• Network Geometry
• Machine learning meets network science: dimensionality reduction for fast and efficient embedding of networks in the hyperbolic space
• Network Mapping by Replaying Hyperbolic Growth
• Curvature and temperature of complex networks
• Multiscale unfolding of real networks by geometric renormalization
• Currency and commodity metabolites: Their identification and relation to the modularity of metabolic networks
• Geometric renormalization unravels self-similarity of the multiscale human connectome
• Network Geometry Inference using Common Neighbors
• Clustering implies geometry in networks
• Navigable Networks as Nash Equilibria of Navigation Games
• Navigable maps of structural brain networks across species
• Descriptive vs. inferential community detection in networks: pitfalls, myths, and half-truths
• Link prediction with hyperbolic geometry
• Soft communities in similarity space
• Disentangling homophily, community structure and triadic closure in networks
• Clustering of random scale-free networks
• Sparse Maximum-Entropy Random Graphs with a Given Power-Law Degree Distribution
• The diameter of KPKVB random graphs
• Detecting hyperbolic geometry in networks: why triangles are not enough
• A geometry-induced topological phase transition in random graphs
• Optimisation of the coalescent hyperbolic embedding of complex networks

Cited by in corpus (2)

• Network Renormalization
• Multiplexity amplifies geometry in networks