Rotated multifractal network generator

TL;DR

This paper introduces a rotation-based transformation to the multifractal network generator to reduce node isolation issues, enhancing the generation of more realistic random graphs.

Contribution

It proposes a simple rotation method for the link probability measure to mitigate node isolation in the multifractal network generator.

Findings

Rotation reduces isolated nodes in generated networks.

The method links the node isolation to the information dimension of the measure.

Improves the realism and diversity of generated network structures.

Abstract

The recently introduced multifractal network generator (MFNG), has been shown to provide a simple and flexible tool for creating random graphs with very diverse features. The MFNG is based on multifractal measures embedded in 2d, leading also to isolated nodes, whose number is relatively low for realistic cases, but may become dominant in the limiting case of infinitely large network sizes. Here we discuss the relation between this effect and the information dimension for the 1d projection of the link probability measure (LPM), and argue that the node isolation can be avoided by a simple transformation of the LPM based on rotation.