The complex structure of the pharmacological drug-disease network

The complexity of drug-disease interactions is a process that has been explained in terms of  the need for new drugs and the increasing cost of drug development, among other factors. Over the last years, diverse approaches have been explored to understand the drug-disease relationships. Here, we construct a bipartite graph in terms of active ingredients and diseases based on thoroughly classified data from a recognized pharmacological website. We find that the connectivities between drugs (outgoing links) and diseases (incoming links) follow approximately a stretched-exponential function with different fitting parameters; for drugs it is between an exponential and power law functions, while for diseases the behaviour is purely exponential. The network projections, onto either drugs or diseases, revealed that the co-ocurrence of drugs (diseases) in common target diseases (drugs) lead to the appearance of connected components, which varies as the threshold number of common target diseases (drugs) is increased. The corresponding projections built from randomized versions of the original bipartite networks were considered to evaluate the differences. The heterogeneity of association at group level between active ingredients  and diseases was evaluated in terms of the Shannon entropy, revealing that higher levels of diversity are present for diseases compared to drugs. Finally, the robustness of the original bipartite network was evaluated in terms of most-connected nodes removal (direct attack) and random removal (random failures).