Identification of missing higher-order interactions in complex networks

Abstract Link prediction has always played a crucial role in unveiling the structural patterns and evolutionary rules of networks. However, as research on complex networks has progressed, the limitations of solely exploring low-order structures have become increasingly apparent. The introduction of high-order organizational theories has not only enriched the conceptual framework of network dynamics but also opened new avenues for investigating the mechanisms of network evolution and adaptation. The complexity and richness of high-order networks pose challenges for link prediction. This study introduces two novel approaches to forecast links in higher-order networks. The first one is to predict links directly in higher-order networks (LPHN), which directly predicts missing links within the higher-order network based on its structure; the other one is to predict higher-order links via link prediction in low-order networks(PHLN), which starts by predicting absent links in a low-order network. Subsequently, the inferred low-order structure is employed as a foundation to extrapolate and reconstruct the predicted higher-order network. Upon comparing the higher-order networks generated by both LPHN and PHLN with the original higher-order networks constructed directly from low-order networks, we discovered that the higher-order networks produced by PHLN exhibit greater accuracy and exhibit a more similar scale of giant components to the original higher-order network. Consequently, the PHLN demonstrates enhanced precision in forecasting the structure of higher-order networks while preserving networks’ structural integrity. Moreover, PHLN exhibits superior performance in the context of large-scale and sparsely connected networks.