Recursive graphs with small-world scale-free properties

TL;DR

This paper introduces recursive clique trees that exhibit small-world and scale-free properties, allowing precise control over clustering and degree distribution, and analyzes their key structural characteristics.

Contribution

It presents a new class of recursive graphs with tunable properties, generalizing existing models and providing detailed analysis of their structural features.

Findings

Graphs have small-world and scale-free characteristics.

The degree distribution follows a power-law with tunable exponent.

The graphs' diameter and clustering can be precisely controlled.

Abstract

We discuss a category of graphs, recursive clique trees, which have small-world and scale-free properties and allow a fine tuning of the clustering and the power-law exponent of their discrete degree distribution. We determine relevant characteristics of those graphs: the diameter, degree distribution, and clustering parameter. The graphs have also an interesting recursive property, and generalize recent constructions with fixed degree distributions.