| Περίληψη: | <p>Many real-world applications in the social, biological, and physical sciences involve large systems of entities that interact together in some way. The number of components in these systems can be extremely large, so some simplification is typically needed for tractable analysis. A common representation of interacting entities is a network. In its simplest form, a network consists of a set of nodes that represent entities and a set of edges between pairs of nodes that represent interactions between those entities. In this thesis, we investigate clustering techniques for time-dependent networks.</p> <p>An important mesoscale feature in networks is communities. Most community-detection methods are designed for time-independent networks. A recent framework for representing temporal networks is multilayer networks. In this thesis, we focus primarily on community detection in temporal networks represented as multilayer networks. We investigate three main topics: a community-detection method known as multilayer modularity maximization, the development of a benchmark for community detection in temporal networks, and the application of multilayer modularity maximization to temporal financial asset-correlation networks. We first investigate theoretical and computational issues in multilayer modularity maximization. We introduce a diagnostic to measure <em>persistence</em> of community structure in a multilayer network partition and we show how communities one obtains with multilayer modularity maximization reflect a trade-off between time-independent community structure within layers and temporal persistence between layers. We discuss computational issues that can arise when solving this method in practice and we suggest ways to mitigate them. We then propose a benchmark for community detection in temporal networks and carry out various numerical experiments to compare the performance of different methods and computational heuristics on our benchmark. We end with an application of multilayer modularity maximization to temporal financial correlation networks. </p>
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