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.