A program generating homogeneous random graphs with given weights

TL;DR

This paper introduces a software tool for generating homogeneous random graphs with user-defined degree-based weights, applicable to various graph types and statistical ensembles, facilitating research in network modeling.

Contribution

The paper presents a novel program package that generates weighted homogeneous random graphs with customizable node degree functions across multiple ensemble types.

Findings

Supports generation of simple graphs and pseudo-graphs

Allows user-defined weight functions for node degrees

Operates across micro-canonical, canonical, and grand-canonical ensembles

Abstract

We present a program package which generates homogeneous random graphs with probabilities prescribed by the user. The statistical weight of a labeled graph $\alpha$ is given in the form $W(\alpha)=\prod_{i=1}^N p(q_i)$, where $p(q)$ is an arbitrary user function and $q_i$ are the degrees of the graph nodes. The program can be used to generate two types of graphs (simple graphs and pseudo-graphs) from three types of ensembles (micro-canonical, canonical and grand-canonical).