Multilayer networks aim at providing a generalized way to deal with longexisting complex social phenomena that, over the years, have been observed using many different approaches. These phenomena have been described using the most diverse terminology belonging to different research areas, but they can be broadly grouped within three domains of problems: heterogeneity of relational ties, heterogeneity of actors, and interdependency between relations. After a short overview of these problems, which give ground for the development of multilayer social networks, in Section 2.1, we describe terminology and a mathematical model that constitute a foundation for all the measures and methods presented in the remainder of the book. Section 2.2 provides an overview of related models that have, in various ways, dealt with similar problems, and Section 2.3 describes a list of available data sets that the reader can explore and study using multilayer networks. All the terms introduced in this chapter, together with other basic terms in graph theory, SNA, and network science, are summarized in the glossary.

Modeling heterogeneity of social relations is an old problem that has often been addressed through qualitative approaches, not only within the borders of SNA. A classical example is the work by Gluckman (1955) that identifies the multiplexity of an African ethnic group's relations (the Lozi people) and defines it as the characteristic of being connected through multiple interdependent social ties. Multiplexity emerges, in Gluckman's work, as the key element to understanding how individuals are part of more complex social structures. This approach has already moved beyond a simple structural analysis to describe the complex system of interdependent relations that Burt and Schott (1989) indicate as the substantive content of personal relationships. Within this perspective, multiplexity is not just an interesting but remote characteristic of social networks but rather the key element to understanding social structures and how individuals are connected. Heterogeneity of social relations maintains its centrality in the SNA field and has been indicated as the characteristic that defines the specific nature of SNA when compared to general network analysis (Borgatti et al., 2009).