Understanding how both the partitions of a bipartite network affect its one-mode projection

TL;DR

This paper investigates how the degree distribution of both partitions in a bipartite network influences its one-mode projection, revealing a strong effect of the second partition's DD through theoretical derivations and simulations.

Contribution

It demonstrates that the degree distribution of the non-target partition significantly impacts the one-mode projection, providing exact and approximate formulas for its DD.

Findings

The DD of the other partition strongly influences the projection's DD.

Derived closed-form formulas for the projection's DD using generating functions.

Validated results through simulations.

Abstract

It is a well-known fact that the degree distribution (DD) of the nodes in a partition of a bipartite network influences the DD of its one-mode projection on that partition. However, there are no studies exploring the effect of the DD of the other partition on the one-mode projection. In this article, we show that the DD of the other partition, in fact, has a very strong influence on the DD of the one-mode projection. We establish this fact by deriving the exact or approximate closed-forms of the DD of the one-mode projection through the application of generating function formalism followed by the method of iterative convolution. The results are cross-validated through appropriate simulations.