Before revision: A plethora of real-world problems require utilization of hypergraphs and diffusion algorithms.Examples include recommendation systems, node ranking in food networks and community detection in social networks to mention a few. Due to the increased size and complexity of real hypergraphs, local and accurate diffusion algorithms that work with the most complex hypergraphs are in need. We propose the first local diffusion method that works on higher-order relations with only a submodularity assumption .
After revision: Recently, hypergraphs have attracted a lot of attention due to their ability to capture complex relations among entities. The insurgence of hypergraphs has resulted in data of increasing size and complexity that exhibit interesting small-scale and local structure, e.g., small-scale communities and localized node-ranking around a given set of seed nodes. Popular and principled ways to capture the local structure are the local hypergraph clustering problem and related seed set expansion problem. In this work, we propose the first local diffusion method that works on higher-order relations with only a submodularity assumption .