Before revision:  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 .
After revision:  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 test and retaining only the statistically significant links. Finally, to test our method we analyze 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 .