Nonparametric network summaries

This thesis is concerned with improving the interpretability of network summaries in both a theoretical and an applied framework, with an application to clinically relevant problems in neuroscience. The theoretical part of this thesis is concerned with graphon estimation using community detection focussed on clustering edge variables instead of nodes. The applied part deals with improving the explainability of the classification of comatose patients according to the topology of their functional connectivity of the brain derived from electroencephalography (EEG) data.

In the first part, we focus on extending the notion of community detection beyond traditional node-centric approaches, i.e. clustering nodes. We propose the stochastic shape model (SSM), a novel framework within graphon estimation that clusters edge variables rather than nodes, thus uncovering what we call edge communities capable of capturing various structures within a network. We refer to such an approach as edge-centric. We further introduce the elongated stochastic shape model, which adaptively controls the structure of the shapes, allowing control over the balance between model complexity and interpretability. We also generalise our result to sparse networks.

In the second part, we turn to an application in clinical neuroprognostication. We develop an explainable machine learning pipeline that uses weighted functional connectivity derived from electroencephalography (EEG) recordings of comatose patients. By preserving the full range of edge weights, rather than binarising connections, the approach captures essential information and avoids discarding subtle but potentially important signals. Furthermore, by integrating features from multiple frequency bands into a single model, the pipeline provides a more complete picture of brain dynamics, leading to improved predictive power. Designed with clinical implementation in mind, this pipeline is widely deployable for any weighted functional connectivity setting, as it uses standard EEG data and emphasises transparency. In particular, the Shapley values highlight the most influential topological features for each individual prediction, increasing the trust of clinicians and facilitating informed decision-making.

The thesis is structured into three parts. Part I (Chapters 1â 2) introduces the foundations of network analysis and graphon-based modelling, highlighting existing challenges and the motivation to shift from node-centric to edge-centric perspectives. Part II (Chapters 3â 4) formally develops the stochastic shape model and its elongated extension, providing theoretical guarantees, including rate optimality, and demonstrating the advantages of models for community detection in complex network structures. Part III (Chapters 5â 6) applies these network-based insights in a neurocritical care setting, where we show how explainable machine learning techniques, combined with weighted functional connectivity analysis, can offer