Modelling populations of complex networks

Many real-life systems can be modelled as complex networks, where the agents of the system are represented as nodes and the ties between those agents are represented as edges. Recent advances in data collection technologies give rise to various populations of networks, which capture different aspects of the data. In this thesis we make an essential progress in the modelling and analysis of three different populations of complex networks. First, in real-life systems involving measurements obtained from a population of participants, the system may be described by a population of networks where each participant is himself described by a whole network. We formulate a relevant genomics problem by constructing such a population of complex networks, and address a series of biological hypothesis which involve the clustering and classification of this population of networks. Second, real-life situations are modelled as a multiplex network where each layer of the multiplex captures different type of relationships across the same set of nodes. The nature of the multiplex network raises the question of whether the same connectivity patterns fit all layers. We use a community detection procedure to address this problem, where random walks on the multiplex are used to detect shared and non-shared community structures across the layers of the multiplex. Third, the interactions between the entities of a system that evolve in time are formalized as a temporal network. When the number of entities in the network is very large, different levels of detail and how they change in time are interesting. We use a multi-scale community detection procedure to solve the problems by applying spectral graph wavelets on the temporal network to detect changes in the community structure that occur in more than one scale.Open Acces