Planar unclustered graphs to model technological and biological networks

TL;DR

This paper introduces a family of deterministic, nearly planar graphs with properties like power-law degree distribution, modularity, and small-world characteristics, useful for modeling complex technological and biological networks.

Contribution

The paper presents a new family of deterministic graphs with tunable parameters that replicate key properties of real-world networks, including planarity and low clustering.

Findings

Graphs have exact formulas for degree distribution and diameter.

Models exhibit small-world and scale-free properties.

Suitable for simulating technological and biological networks.

Abstract

Many real life networks present an average path length logarithmic with the number of nodes and a degree distribution which follows a power law. Often these networks have also a modular and self-similar structure and, in some cases - usually associated with topological restrictions- their clustering is low and they are almost planar. In this paper we introduce a family of graphs which share all these properties and are defined by two parameters. As their construction is deterministic, we obtain exact analytic expressions for relevant properties of the graphs including the degree distribution, degree correlation, diameter, and average distance, as a function of the two defining parameters. Thus, the graphs are useful to model some complex networks, in particular technological and biological networks.