A Simple and Generic Paradigm for Creating Complex Networks Using the Strategy of Vertex Selecting-and-Pairing

TL;DR

This paper introduces a simple, versatile method for generating complex networks by selecting and pairing vertices based on probability distributions, enabling the creation of various network types including scale-free, small-world, and real-world networks.

Contribution

It presents a generic vertex selecting-and-pairing paradigm that can produce diverse complex networks with different degree distributions, surpassing existing methods' limitations.

Findings

Successfully generated multiple synthetic scale-free and small-world networks.

Able to replicate degree distributions of real-world email networks.

Demonstrated versatility across different network models.

Abstract

In many networks of scientific interest we know that the link between any pair of vertices conforms to a specific probability, such as the link probability in the Barab\'asi-Albert scale-free networks. Here we demonstrate how the distributions of link probabilities can be utilized to generate various complex networks simply and effectively. We focus in particular on the problem of complex network generation and develop a straightforward paradigm by using the strategy of vertex selecting-and-pairing to create complex networks more generic than other relevant approaches. Crucially, our paradigm is capable of generating various complex networks with varied degree distributions by using different probabilities for selecting vertices, while in contrast other relevant approaches can only be used to generate a specific type of complex networks. We demonstrate our paradigm on four synthetic Barab\'asi-Albert scale-free networks, four synthetic Watts-Strogatz small-world networks, and on a real email network with known degree distributions.