Emergence of a non-scaling degree distribution in bipartite networks: a numerical and analytical study

TL;DR

This paper investigates the degree distribution in bipartite networks with one fixed partition, analyzing how different attachment mechanisms influence network structure through analytical and numerical methods.

Contribution

It provides exact and approximate analytical expressions for degree distributions under various attachment rules in bipartite networks with one fixed node set.

Findings

Degree distribution varies from binomial to u-shaped depending on attachment type

Exact formulas derived for sequential edge addition

Four regimes identified based on attachment weight

Abstract

We study the growth of bipartite networks in which the number of nodes in one of the partitions is kept fixed while the other partition is allowed to grow. We study random and preferential attachment as well as combination of both. We derive the exact analytical expression for the degree-distribution of all these different types of attachments while assuming that edges are incorporated sequentially, i.e., a single edge is added to the growing network in a time step. We also provide an approximate expression for the case when more than one edge are added in a time step. We show that depending on the relative weight between random and preferential attachment, the degree-distribution of this type of network falls into one of four possible regimes which range from a binomial distribution for pure random attachment to an u-shaped distribution for dominant preferential attachment.