Higher-Order Networks and Dynamics

Project Information

BeyondTheEdge

Grant agreement ID: 101120085

DOI

10.3030/101120085

EC signature date 8 November 2023

Start date 1 January 2024

End date 31 December 2027

Funded under

• Marie Skłodowska-Curie Actions (MSCA)

Total cost

No data

EU contribution

€ 2 553 739,20

Coordinated by

STICHTING VU
Netherlands

Periodic Reporting for period 1 - BeyondTheEdge (Higher-Order Networks and Dynamics)

Reporting period: 2024-01-01 to 2025-12-31

Summary of the context and overall objectives of the project

The scientific aim of the MSCA-DN BeyondTheEdge is to identify the role of nonpairwise ‘higher-order’ interactions in the emergence of complex dynamical behaviour of networks of interacting units. Traditionally, networks are equated with graphs that consist of units together with edges as pairwise relations between two units. However, in network dynamical systems, nonlinear higher order interactions between more than two units often play a critical role in shaping the collective dynamical behaviour of all units: For example, the spread of a disease depends not only on behaviour as pairs of individuals but also how we behave in groups of more than two. Thus, elucidating the role of these higher-order interactions is critical to understand and control the behaviour of complex systems that determine our lives and livelihoods, whether it is the spreading of a lethal disease or the proper functioning of the human brain as a network of billions of interconnected neurons.

The main objective of BeyondTheEdge is to identify the role of nonpairwise ‘higher-order’ interactions in network dynamics by crossing the boundaries of the three emergent themes of foundations, structure, data. To summarize, the consortium is addressing the following three research objectives through its three scientific work packages (WP):

O1 Cutting across structure and foundations (WP1). We will develop the foundations of a mathematical theory for the network dynamical systems on hypergraphs. Since network dynamical systems with higher-order interactions are a specific class of dynamical systems, we will address the following questions: How can we make best use of existing theory for statements about network dynamical systems, and in particular the role of higher-order interactions represented by a hypergraph? Conversely, can we develop new mathematical theory tailored to this (nongeneric) class of dynamical systems based on structural properties?

O2 Cutting across foundations and data (WP2). We will develop data-driven approaches for network dynamics with higher order interactions: Since trajectories of network dynamical systems yield timeseries data, we will address the following questions: What (network) dynamical systems are compatible with given data? Conversely, how can we exploit the (higher-order) network structure to optimally influence/control the dynamics and associated data?

O3 Cutting across data and structure (WP3). We will elucidate what structures (graphs, hypergraphs, etc) are appropriate to understand properties of (dynamical) data. Since graphs/hypergraphs are often convenient representations for data, we will address the questions: For given data—such as data from neural recordings—how can we extract higher-order interaction? Conversely, what do these higher-order features capture and in which cases are representations using graphs sufficient?

Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far

The initial phase of the project (M1–10; Jan 2024–Sept 2024) focused on recruitment and setting up “infrastructure”. Candidate selection was completed in Sept 2024 but formalities (including visas and degree validation continued for several months in some cases). In the meantime, the consortium set up corresponding “infrastructure”, including a professional website (https://BeyondTheEdge.network) which now provides the external “face” of the consortium, social media accounts, mailing lists, and administrative structures to communicate within and across the consortium.

BeyondTheEdge’s research program started with the Kick-Off Meeting at the Vrije Universiteit Amsterdam (VUA) as the coordinating institution. The meeting brought together a large part of the consortium and consisted of dedicated training sessions for PhDs (e.g. Scientific Integrity and Writing, Open Science) as well as for supervisors, the first meeting of the Supervisory Board, and a workshop with expert speakers inside and outside of the consortium.

The first research phase covered by this report (M11–24) yielded progress towards BeyondTheEdge’s research objectives This scientific progress in this initial 13 months has led to three preprints and research papers directly linked to the work by our PhD students by the end of the reporting period. In the meantime, there has been progress towards the training objectives of the consortium. First, BeyondTheEdge created four training courses that were held at the first Network Symposium (May 2025; online) and the second Network Workshop (Oct 2025; at beneficiary AMU in Marseille). The lecture material is openly available through BeyondTheEdge’s website and YouTube channels. Second, by exchanging ideas with invited speakers at the BeyondTheEdge events and being visible at international conferences central to the field, the PhD students were brought to the edge of current research. Third, hands-on training through a hackathon at the second Network Workshop in Marseille added to practical training.

Despite the research program being months away from completing its first half, BeyondTheEdge has left a mark in the community and beyond to realize impact. Highlights include:

Conceptualization of a children’s book “Bear Networks” to bring networks and dynamics even to the smallest (https://doi.org/10.5281/zenodo.11190872).

The BeyondTheEdge online seminar series brings together key speakers in the field.

BeyondTheEdge was featured in the PI’s plenary talk at the SIAM Conference on Applied Dynamical Systems (1100+ delegates).

BeyondTheEdge hosted plenary speaker and a Focus Session on “Network Dynamical Systems” including higher-order interaction networks at NetSci 2025 (800+ delegates), a key conference in network science.

BeyondTheEdge researchers have been active in organizing events and given various invited talks in the community.

Overall, the project is well on track, and all deliverables have been submitted on time.

Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far)

Not applicable at this time