Machine Learning for Static and Single-Event Dynamic Complex Network Analysis

Networks are prevalent data structures that naturally express complex systems. They emerge across a multitude of scientific domains, including physics, sociology, the science of science, biology, neuroscience, and more. In these disciplines, networks illustrate diverse interactions and systems: spin glasses in physics, social connections in sociology, academic collaborations, protein-to-protein interactions in biology, and both structural and functional brain connectivity in neuroscience, to name a few. Due to their complexity and inherently high-dimensional discrete nature, accurately characterizing network structures is both non-trivial and challenging. In recent years, Graph Representation Learning (GRL) has achieved remarkable success in the study of networks, establishing itself as the leading method for network analysis. In general, GRL aims to create a function that can successfully map a network to a low-dimensional latent space through a learning process. Such a mapping defines representations that can be very useful for conducting various downstream tasks, and importantly for helping us to further our understanding of complex networks and their underlying structures. The primary objective of this thesis is to develop novel algorithmic approaches for Graph Representation Learning of static and single-event dynamic networks. In such a direction, we focus on the family of Latent Space Models, and more specifically on the Latent Distance Model which naturally conveys import network characteristics such as homophily, transitivity, and the balance theory. Furthermore, this thesis aims to create structural-aware network representations, which lead to hierarchical expressions of network structure, community characterization, the identification of extreme profiles in networks, and impact dynamics quantification in temporal networks. Crucially, the methods presented are designed to define unified learning processes, eliminating the need for heuristics and multi-stage processes like post-processing steps. Our aim is to delve into a journey towards unified network embeddings that are both comprehensive and powerful, capable of characterizing network structures and adeptly handling the diverse tasks that graph analysis offers.