What Is... a Multilayer Network?

The simplest type of network, which I show in Figure 1, is a graph G = (V,E) [3], where the nodes (or “vertices”) are elements of the set V of N entities in a network and E ⊆ V×V is a set of edges (or “links” or “ties”) that encode pairwise interactions between the entities. A graph can be either undirected or directed. One can encode the information in a graph G as an N×N adjacency matrix A, whose entry Aij is equal to 1 if there is an edge from node i to node j and is otherwise equal to 0. In an undirected network, Aij = 1 if and only if Aji = 1. One can learn a lot about a graph G, and about many dynamical processes on it, by studying the properties (e.g., the eigenvalues) of its associated adjacency matrix A. One can also assign