Weighted and temporal networks: Towards more realistic representations of complex systems

Complex systems consisting of large numbers of interacting elements often display emergent behavior, which cannot be understood by the reductionistic approach of describing the elements and interactions in detail and in isolation. The complex networks framework takes a completely opposite approach by describing the elements and interactions as simply as possible focusing on the system-level behavior instead. This approach has been successful in identifying basic structural properties of systems from various fields such as biology, sociology, neuroscience, and technology. However, this very simplicity of description that makes the complex networks approach so versatile is also its main stumbling block. This is because for many systems, details of individual interactions such as their strengths or timings are essential. Some of such details can be taken into account with weighted and temporal networks. These ways of looking at networks are still fairly underdeveloped; however, there is currently intensive research, especially on temporal networks. The contribution of this Thesis can be divided to three parts: First, it deepens the understanding of many multiscale phenomena in complex networks such as community structure, percolation, and social network formation. Second, it expands the borders of weighted network analysis, amongst others by pointing out the problem that many existing methods for studying cluster structure in weighted networks are domain-specific, instead of being generally applicable to all systems. It also introduces an improvement to clique percolation, which is a non-parametric method for finding cluster structure in weighted networks, that makes it more powerful both computationally and in describing the clusters. Third, it introduces new concepts and methods related to the emerging field of temporal networks and dynamics on top of them. It introduces a systematic way of using reference models to study temporal networks. Using this framework together with a temporal network of mobile communication, it is shown that bursty interaction sequences can slow down dynamics on top of temporal networks, and that such temporal effects can be as important as the network topology.