Inferring monopartite projections of bipartite networks: an entropy-based approach

Abstract

Bipartite networks are currently regarded as providing a major insight into the organization of many real-world systems, unveiling the mechanisms driving the interactions occurring between distinct groups of nodes. One of the most important issues encountered when modeling bipartite networks is devising a way to obtain a (monopartite) projection on the layer of interest, which preserves as much as possible the information encoded into the original bipartite structure. In the present paper we propose an algorithm to obtain statistically-validated projections of bipartite networks, according to which any two nodes sharing a statistically-significant number of neighbors are linked. Since assessing the statistical significance of nodes similarity requires a proper statistical benchmark, here we consider a set of four null models, defined within the Exponential Random Graph framework. Our algorithm outputs a matrix of link-specific p-values, from which a validated projection is straightforwardly obtainable, upon running a multiple hypothesis testing procedure. Finally, we test our method on an economic network (i.e. the countries-products World Trade Web representation) and a social network (i.e. MovieLens, collecting the users' ratings of a list of movies). In both cases non-trivial communities are detected: while projecting the World Trade Web on the countries layer reveals modules of similarly-industrialized nations, projecting it on the products layer allows communities characterized by an increasing level of complexity to be detected; in the second case, projecting MovieLens on the films layer allows clusters of movies whose affinity cannot be fully accounted for by genre similarity to be individuated.

Extracting significant signal of news consumption from social networks: the case of Twitter in Italian political elections

“…The former group is mostly composed of celebrities and official accounts, including politicians, newspapers, etc. Then we identify groups of verified users by their interaction with the opposite layer, following the recipe of [49,50]. If two verified users are retweeted more than expected by non-verified ones, they are likely to be related.…”

Motifs in bipartite ecological networks: uncovering indirect interactions

“…1b). This compression necessarily leads to a substantial loss of information (Zhou et al 2007, Saracco et al 2017. While more sophisticated one-mode projections are available, and these would likely lose less information than the simple projection detailed above, projecting a bipartite network into a unipartite network will always lose some detail.…”

Uncovering indirect interactions in bipartite ecological networks

“…As can be seen in Fig. 1b, this compression necessarily leads to a substantial loss of information (Zhou et al 2007, Saracco et al 2017. For example, interactions with specialist species such as D are not considered as, by definition, specialists only interact with one species.…”