Complex Networks in the Framework of Nonassociative Geometry

Abstract

In the framework of on nonassociative geometry, we introduce a new effective model that extends the statistical treatment of complex networks with hidden geometry. The small-world property of the network is controlled by nonlocal curvature in our model. We use this approach to study the Internet as a complex network embedded in a hyperbolic space. The model yields a remarkable agreement with available empirical data and explains features of Internet connectance data that other models cannot. Our approach offers a new avenue for the study of a wide class of complex networks, such as air transport, social networks, biological networks, etc.

22 pages, 15 figures, accepted version

References in corpus (8)

• Hyperbolic Geometry of Complex Networks
• Sustaining the Internet with Hyperbolic Mapping
• Self-similarity of complex networks and hidden metric spaces
• Emergent Hyperbolic Network Geometry
• Generalized Bose-Fermi statistics and structural correlations in weighted networks
• Curvature and temperature of complex networks
• The Mu2e Experiment
• Discrete Ricci curvatures for directed networks