Multilayer and multiplex networks

Network models that represent multiple kinds of nodes, relationships, or interaction layers within one system. Multiplex networks are a special case in which layers share the same nodes but differ in their relationships.

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Graph theory: The mathematical study of structures made from vertices and edges. Multilayer models extend ordinary graphs by organizing edges and vertices across layers.
Interlayer coupling: A mechanism linking or coordinating activity across layers of a multilayer system. Its strength and structure determine how strongly the layers influence one another.
Social network: A network representing social entities and the relationships among them. People can be connected through separate layers such as friendship, work, and communication.
Simple graph: A graph with no multiple edges between the same vertices and no self-loops. A simple graph has one connection structure, rather than distinct interacting layers.
Adjacency matrix: A matrix whose entries encode which pairs of vertices are connected in a graph. Each layer can be represented by its own adjacency matrix.
Multilayer centrality: A measure of node importance that accounts for connections across multiple network layers. It ranks entities using both within-layer position and cross-layer connectivity.
Transportation network: A network of transport locations connected by routes or services. Road, rail, and air routes form interacting layers of mobility.
Weighted network: A network whose edges carry numerical values representing strength, cost, or intensity. Weights vary connection strength within a layer; they do not by themselves represent different interaction types.
Tensor: A multidimensional array that generalizes vectors and matrices. Tensor notation can encode connections indexed by nodes and layers.
Diffusion on networks: The spread of quantities or states through network connections over time. Diffusion can cross layers and take paths unavailable within any single layer.