Entropy-based methods for the statistical validation of bipartite networks

Bipartite networks provide an insightful representation of many complex systems, ranging from mutualistic species interactions in ecology to financial investment portfolios of banks. In order to unveil genuine properties of real-world structures, statistical comparisons with appropriately defined null models are necessary. Among other frameworks, entropy-based null models have proven to perform satisfactorily in providing benchmarks for testing evidence-based hypotheses, showing the desirable feature that the resulting graph probability distributions are generally unbiased and often analytically tractable. Moreover, applying these models to empirical data permits to reveal “second-order” phenomena by discounting selected topological properties. In this thesis, we present the bipartite exponential random graph formalism and develop a novel method for obtaining unbiased and statistically validated monopartite projections from bipartite networks, the so-called grand canonical projection algorithm. We apply our methods to the social MovieLens database and the International Trade Network, and show that nontrivial communities can be detected in the projections. In particular, in the trade network our approach succeeds in distinguishing between countries of different economic developments and detects a signal of specialization among the general tendency of export diversification. The formalism developed here is general and promises applications in other fields where bipartite structures are present.