Growing Network Models Having Part Edges Removed/added Randomly

TL;DR

This paper introduces new network growth models incorporating random edge modifications, demonstrating scale-free properties through a novel edge-cumulative distribution method that compares non-randomized and randomized networks.

Contribution

The paper develops both non-randomized and randomized network models with fixed motifs, growth, and preferential attachment, and introduces a new method to analyze their scale-free properties.

Findings

The randomized model N'(t) exhibits scale-free behavior.

Edge-cumulative distributions of N(t) and N'(t) are equivalent.

The models capture motif preservation during network growth.

Abstract

Since network motifs are an important property of networks and some networks have the behaviors of rewiring or reducing or adding edges between old vertices before new vertices entering the networks, we construct our non-randomized model N(t) and randomized model N'(t) that have the predicated fixed subgraphs like motifs and satisfy both properties of growth and preferential attachment by means of the recursive algorithm from the lower levels of the so-called bound growing network models. To show the scale-free property of the randomized model N'(t), we design a new method, called edge-cumulative distribution, and democrat two edge-cumulative distributions of N(t) and N'(t) are equivalent to each other.