Combinatorics

Inference

Mathematics

Data mining

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World Wide Web

Machine learning

Copula (linguistics)

Econometrics

Benchmark (surveying)

Artificial intelligence

Geography

Transitive relation

Computer science

Complex network

Proceedings of the National Academy of Sciences

Significance Networks are fundamental units for studying complex systems, but reconstructing networks from large-scale experimental data is very challenging in systems biology and microbial ecology, primarily due to the difficulty in unraveling direct and indirect interactions. By tackling several mathematical challenges, this study provides a conceptual framework for disentangling direct and indirect relationships in association networks. The application of iDIRECT (Inference of Direct and Indirect Relationships with Effective Copula-based Transitivity) to synthetic, gene expression, and microbial community data demonstrates that it is a powerful, robust, and reliable tool for network inference. The framework developed here will greatly enhance our capability to discern network interactions in various complex systems and allow scientists to address research questions that could not be approached previously.

Disentangling direct from indirect relationships in association networks