h1

TY  - THES
AU  - Neuhäuser, Leonie Lisa
TI  - Modelling the effect of groups on network structure and dynamics
PB  - RWTH Aachen University
VL  - Dissertation
CY  - Aachen
M1  - RWTH-2023-08686
SP  - 1 Online-Ressource : Illustrationen, Diagramme
PY  - 2023
N1  - Veröffentlicht auf dem Publikationsserver der RWTH Aachen University
N1  - Dissertation, RWTH Aachen University, 2023
AB  - Networks provide a powerful framework for analysing complex systems in a variety of domains including social, technological and biological systems. In their most basic form, networks represent the components in a system as unlabelled nodes and the interactions between them as pairwise edges. While this abstraction is both simple and expressive, it can fail to capture important aspects of the system - in particular the concept of groups. In this thesis, we explore two different ways in which groups can manifest: Firstly, we consider groups at the macroscopic level in the form of group membership of nodes, meaning that nodes can be grouped based on heterogeneous characteristics. For instance, individuals in social networks differ in certain attributes like gender. From a modelling perspective, group membership can be represented by node labels in an attributed network. Group membership can also affect how nodes form connections and therefore the network structure, for example through tie formation mechanisms such as homophily (nodes tend to connect with nodes in the same group). Examining the network structure is important as it can create structural inequalities which disadvantage certain groups. In the first part of this thesis, we are thus concerned with modelling the impact of group membership on the formation of the network topology. In our first study, we investigate how network structure is affected by biases and errors in the data collection process, many of which are driven by group membership. To this end, we introduce a general model for simulating systematic errors in attributed networks. Using this model on synthetic and real-world networks, we find that the visibility of a minority group, measured in terms of its degree-based ranking position, is strongly affected by systematic errors - and the effects depend on the homophily of the network. In our second study, we then examine how we can improve the visibility of a minority group through different types of interventions. In particular, we introduce a two-phase network growth model where we vary the minority group size or the attachment behaviour of the nodes in the second phase. In general, we find that even extreme group size interventions have a limited impact on minority visibility without accompanying behavioural interventions. Overall, our results from the first part demonstrate the need to model the effect of group membership on the documentation and formation of network structure. By doing so, we can gain a deeper understanding of issues such as inequality and marginalisation through the lens of network analysis. Secondly, we focus on groups at the microscopic level in the form of group interactions, meaning that nodes can interact in groups rather than in pairs. The topology of group interactions can be encoded by hypergraphs in which edges connect an arbitrary number of nodes. Group interactions become particularly relevant when studying dynamical processes. For example, opinion dynamics are often influenced by group phenomena such as peer pressure. To investigate the impact of such group processes, we introduce a novel model for (possibly nonlinear) consensus dynamics on hypergraphs, the Multi-way Consensus Model (MCM). Our analysis reveals that dynamical effects that would not occur in a pairwise system only appear for nonlinear dynamics. In contrast, linear dynamics on hypergraphs can always be written as a pairwise system. This underlines that genuine group effects arise only from the interplay between the group topology of a system and the model of its group dynamics. We then extend MCM to a time-switching topology. In our analysis and simulations, we find interaction effects between multi-body and temporal higher-order facets which additionally impact the dynamics. This emphasises that group interactions and temporal ordering should not be considered in isolation. Finally, we introduce a model for general hypergraph dynamics. We use this model to determine the effective order of a hypergraph dynamical system, which is the minimum order of a hypergraph necessary to approximate the corresponding dynamics accurately. We thus present an effective way to determine how much higher-order information needs to be encoded in a hypergraph dynamical system, both analytically and directly from data. Our method allows researchers to reduce the complexity of their models. In conclusion, the results obtained in this second part emphasise that it is imperative to consider the two aspects of topology and dynamics together when modelling systems with group interactions. Only then is it possible to fully capture higher-order group effects that cannot be investigated by studying pairwise systems.
LB  - PUB:(DE-HGF)11
DO  - DOI:10.18154/RWTH-2023-08686
UR  - https://publications.rwth-aachen.de/record/968617
ER  -