Complex networks: community detection and graph semi-supervised learning on higher-order networks, with an application to the science of science.

Networks represented as graphs with nodes and edges have emerged as effective tools for modeling and analyzing complex systems of interacting entities. Graphs arise naturally in many disciplines, such as social, information, infrastructure, or/and biological networks. However, advances in the study of networked systems have shown that real-world applications often require more sophisticated and diverse representations of interactions. Therefore, higher order interactions have begun to be considered and analyzed in complex networks. Examples of higher-order models include multilayer networks, which represent different type of relationships between the nodes, and simplicial complexes or hypergraphs, which describe collective actions of groups of nodes. In this thesis we deal with the community detection problem on higher-order networks, both in an unsupervised and semi-supervised context. We approach these computational problems applying and adapting optimization methods. Furthermore, we focus on the specific application of collaboration networks in the field of the science of science, analyzing the relation between collaborations and topic switches in time evolving collaboration networks of scholars.