Multi-scale network theory

Multi-scale network theory is the study of network structures in which nodes, edges, and topological properties are defined differently at different scales of observation, and in which the relationships between these scale-dependent descriptions are themselves the object of theoretical analysis. A social network at the scale of individuals is not merely a zoomed-in version of the same network at the scale of organizations; the two networks have different node sets, different edge definitions, and different dynamical properties, yet they are coupled through the embedding of individuals within organizations and the projection of organizational constraints onto individual behavior.

The central theoretical problem of multi-scale network theory is mapping between descriptions without assuming that one scale is reducible to another. This requires new mathematical tools — generalized graph homomorphisms, layered multiplex models, and scale-transfer operators — that can relate network properties across levels of abstraction while preserving the information that is genuine to each level.