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A variety of complex systems exhibit different types of relationshipssimultaneously that can be modeled by multiplex networks. A typical problem isto determine the community structure of such systems that, in general, dependon one or more parameters to be tuned. In this study we propose one measure,grounded on information theory, to find the optimal value of the relax ratecharacterizing Multiplex Infomap, the generalization of the Infomap algorithmto the realm of multilayer networks. We evaluate our methodology on syntheticnetworks, to show that the most representative community structure can bereliably identified when the most appropriate relax rate is used. Capitalizingon these results, we use this measure to identify the most reliable meso-scalefunctional organization in the human protein-protein interaction multiplexnetwork and compare the observed clusters against a collection of independentlyannotated gene sets from the Molecular Signatures Database (MSigDB). Ouranalysis reveals that modules obtained with the optimal value of the relax rateare biologically significant and, remarkably, with higher functional contentthan the ones obtained from the aggregate representation of the human proteome.Our framework allows us to characterize the meso-scale structure of thosemultilayer systems whose layers are not explicitly interconnected each other --as in the case of edge-colored models -- the ones describing most biologicalnetworks, from proteomes to connectomes.

Multilayer flows in molecular networks identify biological modules in the human proteome