Workshop
onModelling and Mining Complex Networks
asHypergraphs(May 15–19, 2023)

Host: Toronto Metropolitan University
Location: Student Learning Centre, DMZ Sandbox (3rd floor)
341 Yonge Street, Toronto, Ontario, Canada M5B 1S1

Organizers:– Bogumil Kamiński (bkamins@sgh.waw.pl)– Pawel Pralat (pralat@torontomu.ca)– François Théberge (theberge@ieee.org)
Sponsors:– Tutte Institute for Mathematics and Computing (TIMC)– Faculty of Science, Toronto Metropolitan University

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Introduction

Hypergraphs have recently emerged as a useful representation for complex networks since
they allow capturing more general relations than graphs. Research on the generalization ofvarious graph-based tools and techniques is booming and, in parallel, new software packages are being developed. Having said that, the theory and tools are still not sufficiently
developed to allow most problems to be tackled directly within this context.
The main goal of the 5 day workshop is to gather together a small group of experts who
specialize on modelling and mining complex networks represented as higher-order structures
such as hypergraphs. Long talks (2 x 75 minutes) in the morning will aim to introduce
specific problems in this context and explain solutions as well as tools used to solve them.
Shorter talks (30 minutes) in the early afternoon will concentrate on open problems andunsolved questions to stimulate collaboration and discussions in the late afternoons andevenings.
There is no registration fee but please let one of us know that you plan to attend(to make sure we have enough space and food). The workshop will include theoreticians
interested in developing theory of hypergraphs, practitioners interested in building ML tools
for hypergraphs, and economists interested in incorporating such solutions in real-world
business applications.

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Schedule

Monday, May 15, 2023
8:55-9:00 Official Opening
9:00-12:00 Leland McInnes, Tutte Institute for Mathematics and Computing
A Whirlwind Introduction to Topological Data Analysis
10:15-10:45 Coffee break
12:00-2:00 Lunch break
2:00-2:30 Megan Dewar, Tutte Institute for Mathematics and Computing
Introduction to the Tutte Institute2:30-3:00 Helen Jenne, Pacific Northwest National Laboratory
Hypergraphs and SVD for Explainable AI
3:00-3:30 Jordan Barrett, Toronto Metropolitan University
Structural properties of ABCD graphs and h-ABCD hypergraphs
3:30-4:00 Coffee break
4:00- Working in groups

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Tuesday, May 16, 2023
9:00-12:00 Nicholas Landry, University of Vermont
Part a) Higher-order interaction networks: structure, dynamics, and inferencePart b) XGI: A Python package for higher-order interaction networks
10:15-10:45 Coffee break
12:00-2:00 Lunch break
2:00-3:30 Yuly Billig, Carleton University
Dense Clusters in Hypergraphs
3:30-4:00 Coffee break
4:00- Working in groups

Wednesday, May 17, 2023
9:00-12:00 Cliff Joslyn and Brenda Praggastis, Pacific Northwest National Laboratory
Hypergraph Modeling and Topological Approaches in HyperNetX
10:15-10:45 Coffee break
12:00-2:00 Lunch break
2:00-3:00 Valérie Poulin, Tutte Institute for Mathematics and Computing
Hypergraph exploration via vectorization
3:00-3:30 Bill Kay, Pacific Northwest National Laboratory
Interpretations of Homology in Hypergraph Analysis
3:30-4:00 Coffee break
4:00- Working in groups3Thursday, May 18, 2023
9:00-12:00 François Théberge, Tutte Institute for Mathematics and Computing
Pawel Pralat, Toronto Metropolitan University
Pawel Misiorek, Poznan University of Technology
Modularity Based Community Detection in Hypergraphs
10:15-10:45 Coffee break
12:00-2:00 Lunch break
2:00-2:30 Leman Akoglu, Carnegie Mellon University
Graph-based Anomaly Detection: Problems, Algorithms and Applications
2:30-3:00 Przemyslaw Szufel, SGH Warsaw School of Economics
Modelling hypergraphs in Julia with SimpleHypgraphs.jl
3:00-3:30 Sebastian Zajac, SGH Warsaw School of Economics
Quantum computing in the context of graphs and hypergraphs
3:30-4:00 Coffee break
4:00- Working in groups
6:00 Dinner

Friday, May 19, 2023
9:00-12:00 Lasse Leskelä, Aalto University
Recovery of communities in sparse and dense hypergraph stochastic block models
10:15-10:45 Coffee break
12:00-2:00 Lunch break
2:00-3:00 Bogumil Kamiński, SGH Warsaw School of Economics
Panel on “Applications of hypergraphs”
3:00-4:00 Coffee break
4:00- Working in groups4

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Participants
1. Leman Akoglu, Carnegie Mellon University, Pittsburgh, US
2. Jordan Barrett, Toronto Metropolitan University, Toronto, Canada
3. Yuly Billig, Carleton University, Ottawa, Canada
4. Winfield Chen, Canoe Financial, Toronto, Canada
5. Megan Dewar, Tutte Institute for Mathematics and Computing, Ottawa, Canada
6. Konstantinos Georgiou, Toronto Metropolitan University, Toronto, Canada
7. Sanaz Gholizadeh, York University, Toronto, Canada
8. Anatoliy Gruzd, Toronto Metropolitan University, Toronto, Canada
9. Reaz Huq, Toronto Metropolitan University, Toronto, Canada

10. Helen Jenne, Pacific Northwest National Laboratory, Seattle, US
11. Cliff Joslyn, Pacific Northwest National Laboratory, Seattle, US
12. Bogumil Kamiński, SGH Warsaw School of Economics, Warsaw, Poland
13. Vinay Kumar, INRIA, France
14. Bill Kay, Pacific Northwest National Laboratory, Seattle, US
15. Nicholas Landry, University of Vermont, Burlington, US
16. Lasse Leskelä, Aalto University, Espoo, Finland
17. Lidan Liao, Toronto Metropolitan University, Toronto, Canada
18. Lukas Lüchtrath, Weierstrass Institute, Berlin, Germany
19. Rehan Malik, Toronto Metropolitan University, Toronto, Canada
20. Trent Marbach, Toronto Metropolitan University, Toronto, Canada
21. Leland McInnes, Tutte Institute for Mathematics and Computing, Ottawa, Canada
22. Pawel Misiorek, Poznan University of Technology, Poznan, Poland
23. Audun Myers, Pacific Northwest National Laboratory, Seattle, US
24. JD Nir, Toronto Metropolitan University, Toronto, Canada
25. Valérie Poulin, Tutte Institute for Mathematics and Computing, Ottawa, Canada
26. Brenda Praggastis, Pacific Northwest National Laboratory, Seattle, US
27. Pawel Pralat, Toronto Metropolitan University, Toronto, Canada
28. Rupan Sampanthan, Toronto Metropolitan University, Toronto, Canada

529. Omair Shafiq, Carelton University, Ottawa, Canada
30. Przemyslaw Szufel, SGH Warsaw School of Economics, Warsaw, Poland
31. François Théberge, Tutte Institute for Mathematics and Computing, Ottawa, Canada
32. Sebastian Zajac, SGH Warsaw School of Economics, Warsaw, Poland
33. Jingwei Zhang, Toronto Metropolitan University, Toronto, Canada
34. Zhiyuan Zhang, Toronto Metropolitan University, Toronto, Canada

4Semi-random List of Places for Lunch Near TMU• Salad King (Thai Cuisine)• GB Hand-Pulled Noodles (Chinese noodle soup)• Paramount Fine Foods (Middle Eastern)• Hokkaido Ramen Santouka (Ramen)• food court at Eaton Center or 10 Dundas East (Cineplex)• JOEY Eaton Center• 3 Brewers• Blaze Pizza• . . . (ask, say, Google for more)

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Semi-random List of Places to See in Toronto• CN Tower (https://www.cntower.ca) Soar above the city at the iconic CN Tower.
Standing 553.3 meters tall, this engineering marvel offers breathtaking views of Toronto’s
skyline. Don’t miss the Glass Floor, SkyPod, and EdgeWalk for an unforgettable experience.
• Royal Ontario Museum (https://www.rom.on.ca) Delve into art, world culture,and natural history at ROM, Canada’s largest museum. Featuring over six million objects, the museum’s exhibits span from ancient civilizations to cutting-edge technology.
The Michael Lee-Chin Crystal is a sight to behold.
• Art Gallery of Ontario (https://www.ago.ca) Home to over 95,000 works, AGO
showcases an impressive collection of Canadian, Indigenous, European, and contemporary art. Witness the creative genius of renowned artists like the Group of Seven,
Vincent van Gogh, and Pablo Picasso.
• Distillery District (https://www.thedistillerydistrict.com) Step back in timeat the Distillery District, a pedestrian-only village adorned with Victorian-era architecture. Boasting art galleries, unique shops, and trendy restaurants, it’s an ideal
place to unwind and enjoy Toronto’s vibrant arts and culture scene.
6• Casa Loma (https://casaloma.ca) Gothic Revival castle-style mansion and garden
in midtown Toronto, Ontario, Canada, that is now a historic house museum andlandmark. It was constructed from 1911 to 1914 as a residence for financier Sir Henry
Pellatt.
• City Cruises Toronto (https://www.citypass.com/toronto/city-cruises-toronto)
Take a break from seeing Toronto by land to see it from the harbour! Discover thehistoric and contemporary sites and nuances of Toronto Harbor during this fun, informative and fully narrated 60-minute Sightseeing Harbour Tour.
• Toronto Island (https://www.torontoisland.com) The Toronto Islands - also called
the Island, or Toronto Island Park - is located in Lake Ontario, a 13-minute ferry ridefrom downtown Toronto. Boats to the Island leave from the Jack Layton Ferry Terminal at the foot of Bay St. and Queen’s Quay. The Island is actually a group of 15
islands inter-connected by pathways and bridges. You can walk from one end of theIsland to the other.
• Music– Toronto Symphony Orchestra (https://www.tso.ca/)– Jazz Bistro (https://jazzbistro.ca/) – Jazz, very close to TMU, more fancy– The Rex (https://www.therex.ca/) – Jazz, more casual• . . . (ask, say, Google for more)

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Abstracts

6.1

A Whirlwind Introduction to Topological Data Analysis

Speaker: Leland McInnes, Tutte Institute for Mathematics and Computing
Abstract
Topological data analysis seeks to bring powerful tools from topology to bear on problems
in data science, helping to elucidate the geometry and structure of diverse data sets. Thismini-course will offer an introduction to relevant topological ideas and approaches, as well
as demonstrating how they can be used in data science to solve real practical problems.
Particular focus will be given to problems in unsupervised learning and exploratory data
analysis where such tools are most effective.

6.2

Introduction to the Tutte Institute

Speaker: Megan Dewar, Tutte Institute for Mathematics and Computing
Abstract
The Tutte Institute for Mathematics and Computing (TIMC) is a government research
institute focused on strategic research in mathematics and computer science, as it applies
to Communication Security Establishment’s (CSE’s) mandate. Our mission is to deliverresearch results having an impact on the most important scientific challenges facing theCanadian and 5-Eyes security and intelligence communities. The TIMC’s key researchareas are cryptography and data science. TIMC occupies a unique position; acting as aninterface between classified and unclassified research organizations linking CSE, secondparties and external research partners (notably, academia and industry). This talk will
present an introduction to the organization; including outlining our mission and ways toengage with us. We will also give an overview of our research activities that may be ofinterest to workshop attendees.

6.3

Hypergraphs and SVD for Explainable AI

Speaker: Helen Jenne, Pacific Northwest National Laboratory
Abstract
Convolutional Neural Networks (CNNs) provide powerful tools for image classification but
are difficult to interpret. At present there is no definitive methodology for linking thefeatures of an input’s domain to a CNN’s decision process and classifications. We approach
this problem by studying the internal dynamics of the network’s convolutional layers using
singular value decomposition. The singular vectors of the weights of a layer align with themost important changes to the internal representations of the input data occurring withinthat layer. Moreover, the natural ordering of the singular values ranks the singular vectors
by the importance of the domain-centric features.
The many-to-many relationships between input images and the singular vectors foundat each layer poses a problem: how do we interpret this data so that we can study the
association between singular vectors and features of the input domain? Our approach uses
hypergraphs to model the relationships between singular vectors and images. In this talk,we show that the combinatorial statistics of hypergraphs are invariant to changes in random
8initial weights and random batch orderings of stochastic gradient descent. This, combinedwith other experiments, suggests that feature learning is independent of training run. We
conclude by demonstrating how our methodology can be used to isolate discriminative features of the input domain. This is joint work with Davis Brown, Brenda Praggastis, andMadelyn Shapiro.

6.4

Structural properties of ABCD graphs and h-ABCD hypergraphs

Speaker: Jordan Barrett, Toronto Metropolitan University
Abstract
The Artificial Benchmark for Community Detection (ABCD) graph is a model for networks
with community structure that exhibit power-law in both their degree distribution andcommunity sizes. The bulk of this talk will introduce the ABCD model and discuss some of
the intricacies of its construction process. We will then briefly introduce the hypergraphABCD (h-ABCD) model and discuss the similarities and differences between the two models.
This talk will act as a preliminary to the talk given later that week, where the ABCD and
h-ABCD models will be discussed more thoroughly.

6.5a) Higher-order interaction networks: structure, dynamics, andinference; b) XGI: A Python package for higher-order interaction networks

Speaker: Nicholas Landry, University of Vermont
Abstract
Part a) In contrast to the assumption that social interactions only involve two individuals
when modeling complex systems, larger interactions often occur in empirical settings. The
collection of these group interactions form a higher-order interaction network.
Higher-order networks are often represented with one of two mathematical objects: (i)hypergraphs and (ii) simplicial complexes. Many null models of higher-order networks either
do not consider the inclusion structure of group interactions or explicitly assume a simplicial
complex. In contrast, empirical datasets do not often exist at either of these extremes, butrather, somewhere in between. We quantify where a dataset lies on this spectrum with ametric we define as ”simpliciality”. We show that existing null models are inadequate forgenerating higher-order networks with the same inclusion structure as empirical datasets.
In addition, we show that the location of the missing subfaces are extremely important forquantifying the simpliciality of a dataset. We introduce null models aimed at bridging the
gap between hypergraph null models and null models of simplicial complexes by specifying
the inclusion structure.
Dynamics on higher-order networks can produce rich behavior, even for very simple
models of contagion. We present two different contagion models: one representing social
contagion and the other describing epidemiological contagion. For the social contagion
model, we focus on the interplay between higher-order structure and the resulting contagion
dynamics of a hypergraph SIS model; in particular, we describe how degree heterogeneity and community structure can affect the onset and existence of tipping-point behavior
and polarization. For the epidemiological model, we describe a reality-inspired model of9environmentally-mediated contagion and present a method to infer network structure andepidemiological parameters from time-series data. We discuss initial work and challenges
applying this model to transmission of C. diff in a hospital setting.
Part b) CompleX Group Interactions (XGI) is a library for higher-order networks, whichmodel interactions of arbitrary size between entities in a complex system. This libraryprovides methods for building hypergraphs and simplicial complexes; algorithms to analyze
their structure, visualize them, and simulate dynamical processes on them; and a collectionof higher-order datasets. XGI is implemented in pure Python and integrates with the restof the Python scientific stack. XGI is designed and developed by network scientists with
the needs of network scientists in mind.
We demonstrate this library’s effectiveness by choosing several higher-order datasets andthen analyzing them. We start by extracting basic statistics of these datasets such as its
size, degree distribution, and density. We also calculate structural measures such as connectedness, assortativity, and centrality and compute different statistics of these metrics. We
show not only how to easily represent higher-order datasets with different data structures,
but also how to use statistics to easily filter datasets. Lastly, we visualize these datasets
using the visualization capabilities of XGI.

6.6

Dense Clusters in Hypergraphs

Speaker: Yuly Billig, Carleton University
Abstract
We solve the problem of finding in a given weighted hypergraph a subhypergraph with amaximum possible density. We introduce the notion of a support matrix and prove thatthe density of an optimal subgraph is equal to |AT A| for an optimal support matrix A.
Alternatively the maximum density of a subgraph is equal to the solution of a minimax
problem for column sums of support matrices. We introduce the spectral decompositionof a hypergraph and show that it is a significant refinement of the Dulmage-Mendelsohn
decomposition. Our theoretical results yield an efficient algorithm for finding the maximum
density subhypergraph and more generally, the spectral decomposition for a given weighted
hypergraph.

6.7

Hypergraph Modeling and Topological Approaches in HyperNetX

Speaker: Cliff Joslyn and Brenda Praggastis, Pacific Northwest National Laboratory
Abstract
The Pacific Northwest National Laboratory in the United States has been supporting a concerted research effort in complex systems modeling incorporating a distinct perspective on
complex networks. Casting complex systems as hypergraphs with an inherent multidimensional topological structure supports multiple missions in analyzing complex informationfrom computational biology, cyber systems, and open-source analytics. In this session wewill first relate the mathematical perspective which informs our modeling approach, including the reliance on attributed hypergraphs with edge- and incidence-specific properties,
multiple topological representations thereof, and the incorporation of these capabilities into10

our HyperNetX (HNX, https://pnnl.github.io/HyperNetX) platform. Recent developments additionally include both the requirement, and the opportunity, to understand how
to marry such high-order network representations to common property graph data models
and engines. With the announcement of HNX 2.0, we will illustrate the methods over asequence of case studies.

6.8

Hypergraph exploration via vectorization

Speaker: Valérie Poulin, Tutte Institute for Mathematics and Computing
Abstract
Text vectorization has undoubtedly become a basic step in natural language processing.
One of its particularities is that it allows for joint embedding of words with sentences orparagraphs in a common space yieldind a distance measure between those different objects.
Inspired by this success, we define a joint embedding of vertices and hyperedges. This
common space offers a mean to perform vertex/hyperedge clustering/classification and hypergraph exploration in general. We will test our vectorization on some benchmark problems
and end this talk with a food for thought question: for which hypergraph problems is vectorization unsuitable?

6.9

Interpretations of Homology in Hypergraph Analysis

Speaker: Bill Kay, Pacific Northwest National Laboratory
Abstract
Cyber analysts use a variety of tools to maintain situational awareness, discover patterns ofuser behavior, and keep their network secure. These tools may be based on known signaturesof behavior or use methods from statistical analysis and machine learning. As adversaries
evolve more complex patterns of behavior, flexible tools that can make sense of complex
changing behavior are needed. Topological Data Analysis is a mathematical method we are
exploring to build such tools. Loosely speaking, topology is the study of data distributed
over space to provide insight into global structure built out of local observations. Examples
of such global structures are loops, voids, and components. With an appropriate space built
from cyber data topological analysis can be performed. As the topology of a cyber networkchanges an analyst can gain insight into the factors that cause these changes. In this talk,we explain various modes of constructing hypergraphs from cyber data and then describe
the topological metrics we use to identify interesting substructures within the data. Finally,
we will show how these topologically-identified substructures were used to gain insight anddraw meaningful conclusions from complex cyber network data.

6.10

Modularity Based Community Detection in Hypergraphs

Speaker: Pawel Misiorek, Poznan University of Technology
Abstract
Part a), François Théberge: The Artificial Benchmark for Community Detection (ABCD)
graph is a recently introduced random graph model with community structure and powerlaw distribution for both degrees and community sizes. In the first part of the talk, we

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introduce a hypergraph counterpart of the ABCD model, h–ABCD.
Part b), Pawel Pralat: The modularity for graphs was first introduced by Newman
and Girvan, and many popular algorithms for partitioning nodes of large graphs use it andperform very well. In the second part of the talk, we generalize it to hypergraphs.
Part c), Pawel Misiorek: The main attraction is a scalable community detection algorithm using hypergraph modularity function. The main obstacle with adjusting the initialstage of the classical Louvain algorithm is dealt via carefully adjusted linear combinationof the graph modularity function of the corresponding two-section graph and the desired
hypergraph modularity function. Bayesian optimization is used to properly tune the algorithm. Finally, the algorithm needs to adjust the weights in the modularity function (in an
unsupervised way), depending on how often nodes in one community share hyperedges withnodes from other communities.

6.11

Graph-based Anomaly Detection: Problems, Algorithms andApplications

Speaker: Leman Akoglu, Carnegie Mellon University
Abstract
Graphs provide a powerful abstraction for representing non-iid data, capturing immediate
as well as long-range relations between various entities. The study of the structure anddynamics of complex graphs has been a central theme of research across various communities.
Graph-based anomaly detection focuses broadly on identifying those ‘constructs’ that do not‘fit’ the expected relational patterns.
This talk will present vignettes from my decade-long research on anomaly detection
using graph-based techniques. I will introduce various scenarios in which graphs can be used
in a natural way – both to formalize concrete anomaly detection problems and to develop
algorithmic solutions that span classical detection methods as well as those leveraging graphneural networks. These will be motivated by real-world applications of anomaly detection
including opinion fraud, accounting anomalies, and host-level intrusion.

6.12

Modelling hypergraphs in Julia with SimpleHypgraphs.jl

Speaker: Przemyslaw Szufel, SGH Warsaw School of Economics
Abstract
SimpleHypergraphs.jl is a flexible library for working with hypergraphs written in the Julia
programming language. SimpleHypergraphs provides several methods for efficient construction, manipulation, and visualization of hypergraphs. The data is stored in a redundant
format (vertices x hyperedges and hyperedges x vertices) for fast access and computationof hypergraph properties. The library also provides ”views” of hypergraphs that implement
an abstraction mechanism required by the popular Graphs.jl library. As of today, Graphs.jl
is one of the fastest graph processing libraries across programming languages. This compatibility makes it possible to run several graph algorithms directly on a bipartite or a
two-section representation of a hypergraph without actually copying the underlying data.
The library also provides several visualization mechanisms, including its implementation on
HTML canvas, support for HyperNetX, as well as GraphPlot.jl available due to Graphs.jl

12compatibility. More information along with tutorials can be found on project’s website athttps://github.com/pszufe/SimpleHypergraphs.jl.

6.13

Quantum computing in the context of graphs and hypergraphs

Speaker: Sebastian Zajac, SGH Warsaw School of Economics
Abstract
Recent years have seen rapid progress in developing quantum computing (QC) devices.
Multiple paradigms have been proposed and implemented in hardware. Still, in the NISQ era(noisy inter-mediate scale quantum) there is an increasing interest in developing algorithm
that requires hybrid quantum-classical approaches. Quantum computing is believed to solve
several problems faster than classical computing in graphs or hypergraphs and in many
optimization problems. For example, the possibility of quantum speedup using the hybrid
quantum approximate optimization algorithm (QAOA) for a max-cut problem is a subjectof active discussion. I will present a realization of the max-cut problem for some simple
graphs that can be computed on quantum simulators and real quantum devices.

6.14

Recovery of communities in sparse and dense hypergraphstochastic block models

Speaker: Lasse Leskelä, Aalto University
Abstract
The accuracy of a community recovery algorithm can be evaluated by running it on benchmark data sets for which the latent community structure is known, but such empiricalapproach is biased by the limited availability of suitable data sets. The hypergraph stochastic block model (HSBM) is a generative model for synthetic hypergraphs associated withan explicit community structure, providing an unbiased benchmark for performance evaluation of community recovery algorithms. In addition to being a simulation workbench, the
HSBM also allows to mathematically analyse the expected accuracy of an algorithm using
the methods of probability theory and statistical information theory.
In this lecture I will discuss fundamental concepts and recent developments on the statistical analysis of hypergraph stochastic block models. In part (a), the focus is on universal
information-theoretic bounds that help to understand requirements on data sparsity andmodel dimensions, under which consistent learning is possible. In part (b), I discuss algorithms that are proven to be consistent in the information-theoretic feasible parameter
regime. Part (c) is devoted to open problems and computational challenges concerning ageneralised non-binary HSBM in which interactions can be of arbitrary type, which allows
to model temporal hypergraphs with time-correlated interaction patterns as a special case.

6.15

Panel on “Applications of hypergraphs”

Moderator: Bogumil Kamiński, SGH Warsaw School of Economics
Panelists (tentative):
1. Cliff Joslyn, Pacific Northwest National Laboratory

132. Nicholas Landry, University of Vermont
3. Lasse Leskelä, Aalto University
4. Brenda Praggastis, Pacific Northwest National Laboratory
5. François Théberge, Tutte Institute for Mathematics and Computing
Abstract
Hypergraphs are natural generalizations of graphs. Therefore they are attractive objectsof theoretical research. At the same time the fact that a hyperedge can join any numberof vertices is a property that is often an important feature in applications that should be
captured by a proper mathematical model.
The flexibility of hypergraphs means that not all concepts and methods developed forgraphs can be easily translated. Researchers and practitioners constantly face novel theoretical and computational problems when studying hypergraphs. This makes this field bothinteresting and challenging.
The objective of the panel is to discuss current opportunities and challenges of practicalapplications of hypergraphs. Together with the panelists we will discuss the following topics:
1. What are currently the most interesting areas of applications of hypergraphs and which
are expected to be most promising in the future?
2. What algorithms and methods are most important to be the focus of the researchcommunity to ensure we have the tools that will be used and useful for practitioners?
3. When doing hypergraph research choosing the right datasets on which the studied
methods should be tested can be a challenge. Does the community need a standard
set of benchmark hypergraphs (both real-world and synthetic benchmarks)?
4. What hypergraphs are encountered in applications (like: number of nodes, degree
distribution, hyperedge size distribution, community structure etc.)?
5. What are the next high-order structures we should look at beyond standard hypergraphs? E.g. directed hypergaphs, simplicial complexes?

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