Random Graph Generator for Bipartite Networks Modeling

The purpose of this article is to introduce a new iterative algorithm with properties resembling real life bipartite graphs. The algorithm enables us to generate wide range of random bigraphs, which features are determined by a set of parameters.We adapt the advances of last decade in unipartite complex networks modeling to the bigraph setting. This data structure can be observed in several situations. However, only a few datasets are freely available to test the algorithms (e.g. community detection, influential nodes identification, information retrieval) which operate on such data. Therefore, artificial datasets are needed to enhance development and testing of the algorithms. We are particularly interested in applying the generator to the analysis of recommender systems. Therefore, we focus on two characteristics that, besides simple statistics, are in our opinion responsible for the performance of neighborhood based collaborative filtering algorithms. The features are node degree distribution and local clustering coeficient.

💡 Research Summary

The paper introduces a novel iterative algorithm designed to generate random bipartite graphs whose structural properties closely resemble those observed in real‑world networks. The motivation stems from the scarcity of publicly available bipartite datasets for testing algorithms in domains such as community detection, influence maximization, and especially recommender systems, where user–item interactions form a natural bipartite structure. Existing random graph generators either focus on unipartite networks or produce bipartite graphs with overly simplistic statistics (e.g., Erdős‑Rényi or basic Chung‑Lu models) that fail to capture two key characteristics identified by the authors as critical for the performance of neighborhood‑based collaborative filtering: (1) the node degree distribution, which in practice follows a heavy‑tailed (often power‑law) pattern, and (2) the local clustering coefficient, reflecting the prevalence of “triadic” structures where two users share a common item (or two items are co‑rated by the same user).

Algorithm Overview
The proposed generator starts from a small complete bipartite seed graph K_{m,n}. At each iteration it either adds a new node to one side of the bipartition or creates a new edge between existing nodes. Edge creation is governed by two probabilistic mechanisms:

1. Preferential Attachment (PA) – a node i is selected with probability proportional to (k_i)^α, where k_i is its current degree and α ∈