Iterative Generation and Generalized Degree Distribution of Higher-Order Fractal Scale-Free Networks

TL;DR

This paper introduces an iterative model for creating higher-order fractal networks, analyzing their fractal properties and scale-free degree distribution through theoretical and experimental methods.

Contribution

It presents a novel iterative generation model for higher-order fractal networks with controllable parameters, expanding understanding of their fractal and scale-free characteristics.

Findings

Networks exhibit fractal properties confirmed by similarity and box-counting dimensions.

Large multiplier m results in scale-free generalized degree distribution.

Model provides a new way to generate and analyze complex higher-order fractal networks.

Abstract

Fractals represent one of the fundamental manifestations of complexity, and fractal networks serve as tools for characterizing and investigating the fractal structures and properties of large-scale systems. Higher-order networks have emerged as a research hotspot due to their ability to express interactions among multiple nodes. This study proposes an iterative generation model for higher-order fractal networks. The iteration is controlled by three parameters: the dimension K of the simplicial complex, the multiplier m, and the iteration count t. The constructed network is a pure simplicial complex. Theoretical analysis using the similarity dimension and experimental verification using the box-counting dimension demonstrate that the generated networks exhibit fractal characteristics. When the multiplier m is large, the generalized degree distribution of the generated networks is characterized by its scale-free nature.