TEMPORAL NETWORK EMBEDDING USING CLASSICAL MULTIDIMENSIONAL SCALING

Thesis Directors: Lluis Arola-Fernández and Lucas Lacasa

Jury: Miguel C. Soriano, Gonzalo Manzano and Lluis Arola-Fernández

Abstract: Temporal networks are becoming widely used in a variety of fields, often as a means of representing complex systems, in which the relationships between the entities are intricate and evolve in time. Processing temporal networks can be cumbersome due to the irregularities and high dimensionality of available network data. These challenges can be addressed by using a temporal network embedding, which aims to coarse-grain detailed temporal network data into a numerical trajectory represented within a low-dimensional space. In this master thesis, a methodology has been proposed that focuses on using Classical Multidimensional Scaling (CMDS) as the way to obtain the network trajectory. With this approach, the embedding is achieved by focusing on the relative distance between the different snapshots that compose the temporal network instead of looking at the structure of each snapshot independently. Our proposed methodology is tested in several synthetic models and empirical network trajectories, where it is shown the Lyapunov exponent and the autocorrelation function are indeed inherited by the embedded network trajectory. These results illustrate how the embedding technique makes it possible to translate concepts from the theory of dynamical systems, such as chaos and memory, to the analysis of empirical temporal networks.