TopoNets 2022

Networks beyond pairwise interactions

Satellite @ Conference on Complex Systems CCS 2022

20 October 2022 - Palma de Mallorca, Spain


The complexity of many biological, social and technological systems stems from the richness of the interactions among their units. Over the past two decades, a great variety of complex systems has been successfully described as networks whose interacting pairs of nodes are connected by links. Yet, from face-to-face human communications to chemical and biological reactions, many interactions in networked systems cannot be described by simple dyads, as they can occur in groups composed by any number of units. Until recently, little attention has been devoted to such high-order architecture of real complex systems. However, a mounting body of evidence is showing that taking the high-order structure of these systems into account can greatly enhance our modelling capacities and help us to understand and predict their emerging dynamical behaviours.

The aim of this satellite is to provide a coherent window on the emerging subfield of networks beyond pairwise interactions. In particular, we will discuss how to represent higher-order interacting systems, and how to unify the diverse frameworks most commonly used to describe higher-order interactions, highlighting the numerous links between the existing concepts and representations. We also focus on recent advancements on the structural measures developed to characterize the structure of these systems, on the related generative models, and on novel emergent phenomena characterizing landmark dynamical processes when extended beyond pairwise interactions.


The Pennsylvania State University, USA

Graph rules and topological insights for inhibitory network dynamics

Grinnell College, USA
Nonbacktracking Spectral Clustering of Nonuniform Hypergraphs

Imperial College, UK

Four ways of going in circles: revisiting directed cycles

Signal processing on cell complexes using discrete Morse theory

Imperial College, UK

High-order statistical phenomena: what are they, and why they matter


[October 20, 2022]

  • 10:00 - 10:15 Welcome and Introduction

  • 10:15 - 11:00 Session I

    • Fernando Rosas

High-order statistical phenomena: what are they, and why they matter
  • 11:00 - 11:30 Coffee Break

  • 11:30 - 12:30 Session II

    • Paul Expert

Four ways of going in circles: revisiting directed cycles
    • Arash Badie-Modiri and Mikko Kivelä

Reticula: A temporal network and hypergraph analysis software package
  • 12:30 - 13:00 Python tutorial

    • Nicholas Landry, Leo Torres

CompleX Group Interactions (XGI): data structures and algorithms for modeling and analyzing complex systems with higher-order (group) interactions
  • 13:00 - 15:15 Lunch Break + CCS Plenary Session

  • 15:15 - 16:15 Session III

    • Nicole Eikmeier

Nonbacktracking Spectral Clustering of Nonuniform Hypergraphs
    • Martina Contisciani, Federico Battiston and Caterina De Bacco

Principled inference of hyperedges and overlapping communities in hypergraphs
  • 16:15 - 16:45 Coffee Break

  • 16:45 - 18:45 Session IV

    • Carina Curto

Graph rules and topological insights for inhibitory network dynamics
    • Florian Klimm

Topological data analysis of truncated contagion maps
  • Jonas L. Juul, Austin R Benson and Jon Kleinberg

Hypergraph patterns and collaboration structure
    • Celia Hacker

Signal processing on cell complexes using discrete Morse theory


All meeting participants need to be registered to the main conference here.


Federico Battiston

Central European University

Iacopo Iacopini

Central European University

Nicholas Landry

University of Vermont

Leo Torres

Max Planck Institute for Mathematics in the Sciences

Francesco Vaccarino

Polytechnic University of Turin


The satellite will have space for contributed talks in the form of 10/15-minute presentations. Participants are invited to submit an abstract in PDF format using the EasyChair website (button below).

Topics of interest relate to higher-order structures (HOrSs) and network topology, and include

  • Higher-order representations of interacting systems

  • Structural measures for HOrS

  • Generative models for HOrS (growing simplicial complexes, bipartite graphs, hypergraphs etc.)

  • Dynamical processes on HOrS (diffusion, spreading, synchronization, games etc.)

  • Applications to real-world systems (TDA)

  • Stochastic topology

  • Topological properties of network embedding into metric or pseudo-metric spaces

  • Topological properties of geometric representations of networks

  • Software and algorithms for HOrSs and TDA

Submissions should be at most 2 pages long (figure included) and should include: title, author(s), and affiliation(s).

Submissions will be evaluated and selected based on the adherence with the theme of the satellite, originality and scientific soundness.

Deadline for submissions: July 20.

Acceptance notifications: July 22.

Authors not already registered on EasyChair should sign up for an account (please note: make sure to use the same email address as the one used for the conference registration).