# A simple bipartite graph projection model for clustering in networks

arXiv: https://arxiv.org/abs/2007.00761 · HTML: https://mlsanity.com/paper/2007.00761/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Jul 2020.

## Built on by (most cited first, 1 of 1)

- [Approximate Decomposable Submodular Function Minimization for Cardinality-Based Components](https://mlsanity.com/paper/2110.14859/) (2021)

## Abstract (arXiv)

Graph datasets are frequently constructed by a projection of a bipartite graph, where two nodes are connected in the projection if they share a common neighbor in the bipartite graph; for example, a coauthorship graph is a projection of an author-publication bipartite graph. Analyzing the structure of the projected graph is common, but we do not have a good understanding of the consequences of the projection on such analyses. Here, we propose and analyze a random graph model to study what properties we can expect from the projection step. Our model is based on a Chung-Lu random graph for constructing the bipartite representation, which enables us to rigorously analyze the projected graph. We show that common network properties such as sparsity, heavy-tailed degree distributions, local clustering at nodes, the inverse relationship between node degree, and global transitivity can be explained and analyzed through this simple model. We also develop a fast sampling algorithm for our model, which we show is provably optimal for certain input distributions. Numerical simulations where model parameters come from real-world datasets show that much of the clustering behavior in some datasets can just be explained by the projection step.