Pattern detection in bipartite networks: a review of terminology, applications, and methods

Rectangular association matrices with binary (0/1) entries are a common data structure in many research fields. Examples include ecology, economics, mathematics, physics, psychometrics, and others. Because their columns and rows are associated to distinct entities, these matrices can be equivalently expressed as bipartite networks that, in turn, can be projected onto pairs of unipartite networks. A variety of diversity statistics and network metrics can be used to quantify patterns in these matrices and networks. But, to be defined as such, what should these patterns be compared to? In all of these disciplines, researchers have recognized the necessity of comparing an empirical matrix to a benchmark ensemble of ‘null’ matrices created by randomizing certain elements of the original data. This common need has nevertheless promoted the independent development of methodologies by researchers who come from different backgrounds and use different terminology. Here, we provide a multidisciplinary review of randomization techniques and null models for matrices representing binary, bipartite networks. We aim at translating concepts from different technical domains to a common language that is accessible to a broad scientific audience. Specifically, after briefly reviewing examples of binary matrix structures encountered across different fields, we introduce the major approaches and strategies for randomizing these matrices. We then explore the details of and performance of specific techniques and discuss their limitations and computational challenges. In particular, we focus on the conceptual importance and implementation of structural constraints on the randomization, such as preserving row and/or columns sums of the original matrix in each of the randomized matrices. Our review serves both as a guide for empiricists in different disciplines, as well as a reference point for researchers working on theoretical and methodological developments in matrix randomization methods.