# Complex Networks in the Framework of Nonassociative Geometry

## TL;DR

This paper introduces a nonassociative geometric model for complex networks, effectively capturing the small-world property and providing insights into Internet structure and other real-world networks.

## Contribution

It presents a novel nonassociative geometric framework that extends statistical models of complex networks, successfully explaining empirical Internet data.

## Key findings

- Model accurately reproduces Internet connectance data
- Nonlocal curvature controls small-world properties
- Applicable to various complex networks

## 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.