Detecting informative higher-order interactions in statistically validated hypergraphs

The increasing availability of new data on biological and sociotechnical systems highlights the importance of well grounded filtering techniques to separate meaningful interactions from noise. In this work the authors propose the first method to detect informative connections of any order in statistically validated hypergraphs, showing on synthetic benchmarks and real-world systems that the highlighted hyperlinks are more informative than those extracted with traditional pairwise approaches. Recent empirical evidence has shown that in many real-world systems, successfully represented as networks, interactions are not limited to dyads, but often involve three or more agents at a time. These data are better described by hypergraphs, where hyperlinks encode higher-order interactions among a group of nodes. In spite of the extensive literature on networks, detecting informative hyperlinks in real world hypergraphs is still an open problem. Here we propose an analytic approach to filter hypergraphs by identifying those hyperlinks that are over-expressed with respect to a random null hypothesis, and represent the most relevant higher-order connections. We apply our method to a class of synthetic benchmarks and to several datasets, showing that the method highlights hyperlinks that are more informative than those extracted with pairwise approaches. Our method provides a first way, to the best of our knowledge, to obtain statistically validated hypergraphs, separating informative connections from noisy ones.