  Complex networks are a powerful paradigm to model complex systems. Specific
network models, e.g., multilayer networks, temporal networks, and signed
networks, enrich the standard network representation with additional
information to better capture real-world phenomena. Despite the keen interest
in a variety of problems, algorithms, and analysis methods for these types of
network, the problem of extracting cores and dense structures still has
unexplored facets. In this work, we present advancements to the state of the
art by the introduction of novel definitions and algorithms for the extraction
of dense structures from complex networks, mainly cores. At first, we define
core decomposition in multilayer networks together with a series of
applications built on top of it, i.e., the extraction of maximal multilayer
cores only, densest subgraph in multilayer networks, the speed-up of the
extraction of frequent cross-graph quasi-cliques, and the generalization of
community search to the multilayer setting. Then, we introduce the concept of
core decomposition in temporal networks; also in this case, we are interested
in the extraction of maximal temporal cores only. Finally, in the context of
discovering polarization in large-scale online data, we study the problem of
identifying polarized communities in signed networks. The proposed
methodologies are evaluated on a large variety of real-world networks against
na\"{\i}ve approaches, non-trivial baselines, and competing methods. In all
cases, they show effectiveness, efficiency, and scalability. Moreover, we
showcase the usefulness of our definitions in concrete applications and case
studies, i.e., the temporal analysis of contact networks, and the
identification of polarization in debate networks.
