2026-08-13 –, Room 5
Many important networks have beyond-binary relations that make graph structures inefficient or insufficient representations. Hypergraphs, the generalizations of traditional graphs, are needed to study such complex networks. In this talk, we will discuss hypergraph modeling in Julia, primarily focusing on SimpleDirectedHypergraphs.jl, a recently developed package for complex networks with n-ary directional relations.
Commonly, researchers and engineers represent various networks — ecological, social, computer, and more — as graphs. However, graphs can encode only binary relations (i.e., edges connect exactly two vertices), making them inappropriate to model many complex networks of technical and research significance. For these cases — including modeling relational databases, financial transfers, and chemical reaction networks — more general hypergraphs are essential tools. In hypergraphs, hyperedges can connect arbitrary numbers of vertices, bypassing the key binary restriction of graphs.
In this talk, we will discuss efforts to represent and model hypergraphs, especially directed hypergraphs, in Julia. We will begin by introducing hypergraphs and their practical utility for network modeling before shifting to hypergraph representations and tools in Julia.
We will briefly discuss SimpleHypergraphs.jl, developed by Przemysław Szufel and colleagues.[1] We will introduce the sparse representation of hypergraphs as matrices, the connection with Graphs.jl, and mention various features and analyses available for undirected hypergraphs.
The bulk of the talk will focus on directed hypergraphs, implemented in the recently developed package SimpleDirectedHypergraphs.jl. We will demonstrate how to construct directed hypergraphs by-hand, from external data, and randomly. We will further introduce a number of algorithms included in SimpleDirectedHypergraphs.jl, in particular focusing on heuristic and exact pathfinding. Our discussion will conclude with a small application involving random and real-world chemical reaction networks.
SimpleDirectedHypergraphs.jl is the first package for directed hypergraph construction and analysis in Julia. To the best of our knowledge, general-purpose directed hypergraph packages are also absent in many high-level programming languages used in mathematics and science (e.g., R, MATLAB), with most available packages focusing exclusively (e.g., hypernetx[2], HyperG) or mainly on undirected hypergraphs (e.g., directed hypergraphs are, at the time of this writing, an "experimental feature" in the Python package XGI). Beyond being an addition to the Julia ecosystem, SimpleDirectedHypergraphs.jl is thus positioned to benefit network science and network scientists broadly.
Notes:
[1]: Antelmi et al., arXiv:2002.04654 2020, DOI: 10.48550/arXiv.2002.04654
[2]: Praggastis et al., arXiv:2310.11626 2023, DOI: 10.48550/arXiv.2310.11626
I'm a teacher-scholar currently based in Dublin, Ireland, where I work at University College Dublin as an Ad Astra Fellow & Assistant Professor of Digital Chemistry. I am also an Adjunct Professor of Chemical Engineering at Carnegie Mellon University. Though my training is in materials science and my professional affiliations are in chemistry and chemical engineering, my research interests are broad, including not only areas of the chemical sciences (e.g., sustainable chemistry, catalysis, electrochemistry, chemical reaction networks) but also network science, data science, pedagogy, philosophy (philosophy of science and ethics), mathematics (combinatorics), and more.
I founded and am currently working to build up the Community of Researchers Assessing Chemical Transformations and Exploring Reactivity (CoReACTER), an anti-oppressive, democratic research collective. I am an active supporter of open-source software, both through my own development efforts and in my work as a Topic Editor for the Journal of Open Source Software. I care deeply about teaching the next generation of scientists and researchers, and I actively seek out opportunities to mentor others, particularly those from marginalized backgrounds.
Outside of my academic work, I love reading, writing, drinking tea, and hiking.
Radiochemist, spectroscopist, and data scientist (kinda). Now a PhD student studying chemical reaction networks and machine learning on directed hypergraphs.