Detecting informative higher-order interactions in statistically validated hypergraphs

Abstract

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 large number of works on networks, highlighting informative hyperlinks in hypergraphs obtained from real world data 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. For all cases, the method highlights hyperlinks that are more informative than those extracted with pairwise approaches. Our method provides a first way to obtain statistically validated hypergraphs, separating informative connections from redundant and noisy ones.

Spectral detection of simplicial communities via Hodge Laplacians

“…In fact if we start from a network, clique community detection makes the assumption that all cliques are filled, i.e., it assumes that each clique indicates a many-body interaction which might not be realistic. Indeed, since simplicial datasets are uncommon, the inference of true many-body interactions starting from the exclusive knowledge of pairwise interactions (a network) has been receiving increasing attention [50,51]. Here we show, by analysing the Zachary Karate club network, that given the ground-truth community of a network, the study of simplicial communities can be turned to an inference algorithm for determining the true higher-order interactions between the nodes of a given network.…”

“…However the true many-body interactions may be captured by a simplicial complex including only a subset of the simplices present in the clique complex (e.g. filling only a subset of all triangles), hence the need to formulate reliable inference methods to detect which cliques of the network correspond to filled simplices such as the ones proposed in [50,51]. As such, a simplicial complex is a subset of a clique complex.…”

The physics of higher-order interactions in complex systems

“…Even when explicit hyperedge data are available, just as with pairwise network data, errors and incompleteness are unavoidable, requiring us to reconstruct the object of study from uncertain observations [66,67]. For hypergraph data, recent work [68] has proposed an approach based on comparisons with null models, which is capable of filtering out hyperedges that are not statistically significant. More work is needed to provide uncertainty quantification on the analyses that are conditioned on the reconstruction, as well as leveraging more advanced techniques of hyperedge prediction to improve accuracy.…”