Multilayer networks

The chapter “Multilayer Networks” introduces the topic of interconnected multilayer networks, analyzing them from a few fronts: types of multilayer networks, their mathematical description, the dynamics of random walks, and the centrality (versatility) of nodes. Multilayer networks appear naturally in real data as, in many cases, the relationships (links) between the elements (nodes) can be of different kinds. For example, people can be connected through friendship, family relations, or work relations. This structure can be represented as a network formed by three layers, one for each type of relationship, with the same nodes repeated in all layers. Thus, there are different behaviors in each layer, and interactions between them, which result in more realistic but, at the same time, more complex dynamics. This chapter shows how interconnected multilayer topology describes such networks more accurately than edge coloring does and introduces the tensor formalism used to construct them.