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Basic Structural Properties

In this chapter the basic structural properties of multilayer networks are given. This chapter reveals that on multilayer networks the most basic structural properties of a network such as the degree or the clustering coefficient are also significantly modified. Therefore, it is necessary to define the multiplex degree and the multiplex degree distribution, the multilayer degree and the multilayer degree distribution, and the multilayer clustering coefficients. The chapter also discusses the relation between the properties of multiplex and multi-slice networks and the corresponding properties of their aggregated network. Finally, the chapter introduces multilayer distance-dependent measures, including generalization of the betweenness centrality (interdependence, cross-betweenness) and of the closeness centrality.