The authors are hosting an AMS sponsored Mathematics Research Community (MRC) focusing on two themes that have garnered intense attention in network models of com- plex relational data: (1) how to faithfully model multi-way relations in hypergraphs, …
Hypergraphs offer flexible and robust data rep- resentations for many applications, but methods that work directly on hypergraphs are not readily available and tend to be prohibitively expensive. Much of the current analysis of hypergraphs relies on …
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 set-valued. To …
We propose a flexible framework for clustering hypergraph-structured data based on recently proposed random walks utilizing edge-dependent vertex weights. When incorporating edge-dependent vertex weights (EDVW), a weight is associated with each …
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 which then …
As data structures and mathematical objects used for complex systems modeling, hypergraphs sit nicely poised between on the one hand the world of network models, and on the other that of higher-order mathematical abstractions from algebra, lattice …
We present the Chapel Hpergraph Library (CHGL), a library for hypergraph computation in the emerging Chapel language. Hypergraphs generalize graphs, where a hypergraph edge can connect any number of vertices. Thus, hypergraphs capture high-order, …
As data accumulate faster and bigger, building representational models has turned into an art form. Despite sharing common data types, each scientific discipline often takes a different approach. In this work, we propose representational models …
Network science is a powerful tool for analyzing complex systems in fields ranging from sociology to engineering to biology. This article is focused on generative models of large-scale bipartite graphs, also known as two-way graphs or two-mode …