Related papers: HL-index: Fast Reachability Query in Hypergraphs
We propose high-order hypergraph walks as a framework to generalize graph-based network science techniques to hypergraphs. Edge incidence in hypergraphs is quantitative, yielding hypergraph walks with both length and width. Graph methods…
Hypergraphs are widely adopted tools to examine systems with higher-order interactions. Despite recent advancements in methods for community detection in these systems, we still lack a theoretical analysis of their detectability limits.…
Hypergraphs, encoding structured interactions among any number of system units, have recently proven a successful tool to describe many real-world biological and social networks. Here we propose a framework based on statistical inference to…
We propose that hypergraphs can be used to model social networks with overlapping communities. The nodes of the hypergraphs represent the communities. The hyperlinks of the hypergraphs denote the individuals who may participate in multiple…
This paper considers structures of systems beyond dyadic (pairwise) interactions and investigates mathematical modeling of multi-way interactions and connections as hypergraphs, where captured relationships among system entities are…
Controlling real-world networked systems, including ecological, biomedical, and engineered networks that exhibit higher-order interactions, remains challenging due to inherent nonlinearities and large system scales. Despite extensive…
Since knowledge graphs (KGs) describe and model the relationships between entities and concepts in the real world, reasoning on KGs often correspond to the reachability queries with label and substructure constraints (LSCR). Specially, for…
There is increasing focus on analyzing data represented as hypergraphs, which are better able to express complex relationships amongst entities than are graphs. Much of the critical information about hypergraph structure is available only…
We present a new approach for the approximate K-nearest neighbor search based on navigable small world graphs with controllable hierarchy (Hierarchical NSW, HNSW). The proposed solution is fully graph-based, without any need for additional…
Hypergraphs are generalisation of graphs in which a hyperedge can connect any number of vertices. It can describe n-ary relationships and high-order information among entities compared to conventional graphs. In this paper, we study the…
Real-world complex systems are often better modeled as hypergraphs, where edges represent group interactions involving multiple entities. Understanding and quantifying homophily (similarity-driven association) in such networks is essential…
Hypergraphs, capable of representing high-order interactions via hyperedges, have become a powerful tool for modeling real-world biological and social systems. Inherent relationships within these real-world systems, such as the encoding…
Many networks can be characterised by the presence of communities, which are groups of units that are closely linked. Identifying these communities can be crucial for understanding the system's overall function. Recently, hypergraphs have…
Biharmonic distance (\bd) is a powerful graph distance metric with many applications, including identifying critical links in road networks and mitigating over-squashing problem in \gnn. However, computing \bd\ is extremely difficult,…
Geosocial reachability queries (\textsc{RangeReach}) determine whether a given vertex in a geosocial network can reach any spatial vertex within a query region. The state-of-the-art 3DReach method answers such queries by encoding graph…
Hypergraphs provide a fundamental framework for representing complex systems involving interactions among three or more entities. As empirical hypergraphs grow in size, characterizing their structural properties becomes increasingly…
In this paper we consider aspects of geometric observability for hypergraphs, extending our earlier work from the uniform to the nonuniform case. Hypergraphs, a generalization of graphs, allow hyperedges to connect multiple nodes and…
Higher-order interactions (HOIs) in complex systems, such as scientific collaborations, multi-protein complexes, and multi-user communications, are commonly modeled as hypergraphs, where each hyperedge (i.e., a subset of nodes) represents…
Complex systems frequently exhibit multi-way, rather than pairwise, interactions. These group interactions cannot be faithfully modeled as collections of pairwise interactions using graphs and instead require hypergraphs. However, methods…
Hypergraphs that can depict interactions beyond pairwise edges have emerged as an appropriate representation for modeling polyadic relations in complex systems. With the recent surge of interest in researching hypergraphs, the centrality…