Bipartite networks are currently regarded as providing a major insight into URLanization of real-world systems, unveiling the mechanisms shaping the interactions occurring between distinct groups of nodes. One of the major problems encountered when dealing with bipartite networks is obtaining a (monopartite) projection over 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 . The criterion adopted to quantify the similarity of nodes rests upon the similarity of their neighborhoods : in order for any two nodes to be linked, a significantly-large number of neighbors must be shared. Naturally, assessing the statistical significance of nodes similarity requires the definition of a proper statistical benchmark: here we consider two recently-proposed null models for bipartite networks, opportunely defined through the exponential random graph formalism. The output of our algorithm thus consists of a matrix of  p-values, from which a validated projection can be straightforwardly obtained, upon running a multiple hypothesis testing and linking only the nodes which pass it. We apply our algorithm to social and economic bipartite networks: when projecting the network of countries and exported goods on the countries layer, our method is able to cluster countries with similar a industrialisation; we also analysed a social network  of users and positively-rated movieson the films layer: in this caseour approach divides movies in clusters of similar genres or audience .
Bipartite networks are currently regarded as providing a major insight into URLanization of real-world systems, unveiling the mechanisms shaping the interactions occurring between distinct groups of nodes. One of the major problems encountered when dealing with bipartite networks is obtaining a (monopartite) projection over 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 monopartite projections of bipartite networks , which implements a simple rule : in order for any two nodes to be linked, a significantly-large number of neighbors must be shared. Naturally, assessing the statistical significance of nodes similarity requires the definition of a proper statistical benchmark: here we consider two recently-proposed null models for bipartite networks, opportunely defined through the exponential random graph formalism. Our algorithm outputs a matrix of link-specific p-values, from which a validated projection can be straightforwardly obtained, upon running a multiple hypothesis test and retaining only the statistically significant links. Finally, to test our method we analyze a social network (i.e. the MovieLens dataset, a bipartite network of users and rated movies) and an economic network (i.e. the countries-products World Trade Web representation): while, in the first case, projecting MovieLens on the films layer allows clusters of movies belonging to similar genres to be detected, in the second case, projecting the World Trade Web on the countries layer reveals a modular structure of similarly-industrialized clusters of nations .
A
monopartite
R
. The criterion adopted to quantify the similarity of nodes rests upon the similarity of their neighborhoods
, which implements a simple rule
R
The output of our algorithm thus consists of
Our algorithm outputs
A
link-specific
R
testing and linking only the nodes which pass it. We apply our algorithm to social and economic bipartite networks: when projecting the network of countries and exported goods on the countries layer, our method is able to cluster countries with similar a industrialisation; we also analysed
test and retaining only the statistically significant links. Finally, to test our method we analyze
A
(i.e. the MovieLens dataset, a bipartite network
R
positively-rated movieson the films layer: in this caseour approach divides movies in clusters of similar genres or audience
rated movies) and an economic network (i.e. the countries-products World Trade Web representation): while, in the first case, projecting MovieLens on the films layer allows clusters of movies belonging to similar genres to be detected, in the second case, projecting the World Trade Web on the countries layer reveals a modular structure of similarly-industrialized clusters of nations