PhD Position - BeyondTheEdge Project - Graph vs Hypergraph Metrics

A 3-year PhD position is available within the framework of the Marie Skłodowska-Curie Doctoral Network (MSCA-DN) “BeyondTheEdge”, funded by the European Union’s Horizon Europe Programme.

The candidate will be employed by the University of Zaragoza and enrolled as a PhD student in the Physics Program. The PhD project will be under the supervision of Prof. Yamir Moreno. During the doctoral program, two secondments are expected: 1) at CENTAI Institute, Italy, with Dr. Guilherme Ferraz de Arruda (6 months), and 2) CWTS, The Netherlands, with Dr. Vincent Traag (3 months).

Applications from all groups currently under-represented in academic posts are especially encouraged. We particularly welcome applications from women and people with an ethnic minority background.

General Objective of the MSCA: Many systems that govern our everyday lives—from communication networks to the human brain—can be seen as networks of interconnected units. Traditionally, networks are equated with graphs where edges give 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 our 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 dynamics of complex systems that determine our lives and livelihoods, whether it is the spreading of a disease or the proper functioning of the human brain as a network of billions of neurons.

The doctoral network BeyondTheEdge will identify the role of nonpairwise higher-order interactions in the emergence of complex dynamical behaviour of networks of interacting units. BeyondTheEdge brings together key researchers in an international network that is interdisciplinary (from mathematics to neuroscience) and intersectorial (including academia, private research institutes, and industry) to develop new mathematical insights relevant for real-world problems. BeyondTheEdge will train a cohort of 10 PhD students through research, education, and complementary skills training. This will enable the PhD students to innovate, collaborate, and become leading professionals in academia, industry, or the public sector: Innovative training activities will ensure that all PhD students can apply their skills beyond the academic context and put them in perspective of the wider world. Supervisor training activities ensure that the more junior project partners can shape the PhD education of the future. Thus, BeyondTheEdge will make a lasting contribution that will far outlive the duration of the project.

Specific Objective: The last two decades have witnessed a revolution in the way in which interactions among a system’s constituents are measured and characterized, leading to more realistic and accurate models to describe real-world dynamical processes such as contagion or disease-like dynamics. Recently, evidence have shown that networks are more complex than graphs and that pairwise interactions do not capture many of the key features associated with group and other forms of higher-order interactions (HOIs). These discoveries have shifted the focus on the study of the structure and dynamics of/on hypergraphs. However, despite these advances, most of the metrics that are used to characterise higher-order networks are the same (or untested, direct generalizations) that were developed to characterize graphs, which hinders further advances in the mathematical characterization of real systems and the uncovering of new structures and phenomena associated with higher-order systems.

The main objective of this PhD project is to elucidate when graph metrics are suited to characterize HOIs, both in terms of the structure and the dynamics, and when and which new metrics need to be introduced. We will apply our results to different datasets and processes and unlock new methodological and mathematical tools to better capture the nature and consequences of HOIs. Critical questions are: How is the hypergraph structure relevant? How do HOIs impact dynamics? And are the answers to the previous questions conditioned to the metrics that are used to characterise the graph/hypergraph and the dynamics? We will start by determining how properties of graphs and hypergraphs relate mathematically, identifying in this way what are the metrics that cannot be used to characterize HOIs and what new—not necessarily generalizations of existent—metrics are needed. We will then extend the study to finding relevant order parameters to characterise dynamical processes and phase transitions. We will focus on processes that involve critical-mass dynamics to model social contagion, identifying new descriptors for the system’s critical properties that could not be uncovered using metrics for graphs. Our theoretical framework will be tested on several datasets including contact data and the optimization of task- assignment graphs subject to constraints [Secondment CENTAI] as well as authorship networks [Secondment CWTS]. This project will elucidate when hypergraphs are appropriate to analyse higher-order interactions and what metrics are suitable. Beyond the applications in the secondments, the resulting tools will find applications in robustness, optimization, and control of higher-order systems.

Expected Results: A new theoretical and computational framework with novel metrics to characterize the structure and the dynamics of HOIs described by hypergraphs as well as new mechanistic explanations of critical dynamics, isolating what mechanisms are deeply rooted in the higher-order nature of the interactions. Validation of the new metrics and theoretical methods in at least 3 different datasets or real problems.