Latent geometry of bipartite networks

Maksim Kitsak, Fragkiskos Papadopoulos, and Dmitri Krioukov
Physical Review E
95, 032309
March 8, 2017

Abstract

Despite the  abundance of bipartite networked systems, their organizing principles are  less studied, compared to unipartite networks. Bipartite networks are often  analyzed after projecting them onto one of the two sets of nodes. As a result  of the projection, nodes of the same set are linked together if they have at  least one neighbor in common in the bipartite network. Even though these  projections allow one to study bipartite networks using tools developed for  unipartite networks, one-mode projections lead to significant loss of  information and artificial inflation of the projected network with fully  connected subgraphs. Here we pursue a different approach for analyzing  bipartite systems that is based on the observation that such systems have a  latent metric structure: network nodes are points in a latent metric space,  while connections are more likely to form between nodes separated by shorter  distances. This approach has been developed for unipartite networks, and  relatively little is known about its applicability to bipartite systems.  Here, we fully analyze a simple latent-geometric model of bipartite networks,  and show that this model explains the peculiar structural properties of many  real bipartite systems, including the distributions of common neighbors and  bipartite clustering. We also analyze the geometric information loss in  one-mode projections in this model, and propose an efficient method to infer  the latent pairwise distances between nodes. Uncovering the latent geometry  underlying real bipartite networks can find applications in diverse domains,  ranging from constructing efficient recommender systems to understanding cell  metabolism.

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