Many real-world systems can be represented using complex networks, where the different agents and their relations are represented as nodes and links, respectively. Traditional network models employ simple graphs where the graph is represented by a set of vertices and edges that connect them. With the advances in data acquisition technologies and the different types of data that are available, the simple graph model becomes insufficient to describe the higher dimensional relational data sets. For instance, in social networks, users can be defined as nodes with multiple types of interactions like friendship, collaboration, and economic exchange, connecting them. Furthermore, each node is often associated with attributes such as demographics or interests. To overcome the limitation of existing simple graph models, multi-dimensional graphs such as multiplex networks have been proposed. Similarly, in order to capture the node information that is available in most real-world networks, attributed graphs have been introduced.Given a large scale complex network, one is usually interested in learning the underlying graph structure, such as the community structure or hub nodes. These structures uncover meaningful patterns and provide insights within complex networks. Community detection identifies groups of nodes that are more densely connected to each other than they are to the rest of the network. Hub nodes, on the other hand, correspond to nodes which are densely connected to the rest of the graph and play a critical role in information processing in the network. Although there are numerous works on community detection in single-layer networks, existing work on multiplex community detection mostly focuses on learning a common community structure across layers without taking the heterogeneity of the different layers into account. Beyond detecting communities within a single multiplex network, many applications may require comparing the community structures of two or more multiplex networks. Furthermore, most of the existing community detection methods focus solely on the graph connectivity information. In attributed graphs, where each node is associated with an attribute vector, the community detection methods that focus only on the edges and the data clustering methods that focus only on the attributes of the nodes become insufficient. Traditional hub detection methods rely mostly on graph connectivity without taking the node attributes into account. This thesis addresses the limitations of learning these graph structures in high-dimensionaland attributed networks. Novel algorithms for multiplex and attributed community detection, as well as approaches for discovering discriminative communities between two multiplex networks, are introduced using graph spectral theory and graph signal processing methods. Similarly, a graph signal processing approach that takes into account both the graph topology and node attributes is introduced for hub node identification.
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