The actors in the kinds of networks that social scientists study are very frequently connected by more than one type of tie, simultaneously. That is, the relationship between any two actors may be multiplex. In this chapter, we've introduced a few of the tools that are commonly used to help to make sense of the complex patterns of embedding that can emerge when there is more than one kind of tie operating simultaneously.
Multiplex data are usually stored in a data structure of node-by-node matrices that are "stacked" as "slices" in a single file. Usually, these structures contain slices that measure different relations (e.g. money, information). However, the same data structure can be effectively used to store and work with multiple slices that show the state of the same network at multiple points in time, or the same network as perceived by different observers embedded in it (Cognitive social structures, or CSS). A compact way of storing information about multiple kinds of relations among actors in a single matrix, the multi-valued matrix, uses a number to reflect the qualitative type of relation that exists between two actors (e.g. none, money only, information only, information and money; or mutually exclusive "multiple choice" types like: kin, neighbor, coworker).
With relatively small networks, and relatively small numbers of relations, graphs can be prepared that show the unions nd intersections of multiple kinds of relations, or "animate" change over time in network structure.
Usually the information about multiple kinds of relations among actors is indexed by reducing the multiple ties into a single quantitative value that represents a summary across the separate relations (e.g. average tie strength, maximum, minimum). Alternatively, the information about different kinds of ties may be combined into more complex typologies using logical relations and "role algebra". A special set of tools for dealing with the unique features of CSS data was also discussed.
Many social network studies avoid the complexity of multiplex data by focusing on a single relation, or by dealing with multiple relations separately. There is a good bit of virtue in this, for multiplex analysis can be quite demanding (at least there are many plausible ways of approaching any multi-relational problem). Still, in some cases, engaging the full complexity of multiplex data has pair huge returns. Our understanding of kinship structures, and our understanding of the positions of nation-states in the world system have been greatly enhanced by indexing actors' relational positions based on multiple and simultaneous ties.