Communicability in time-varying networks with memory

Abstract We develop a first-principles approach to define the communicability between two nodes in time-varying network with memory. The formulation is based on time-fractional Schrödinger equation, where fractional (of Caputo type) derivative accounts for memory of system. Using Hamiltonian tight-binding formalism we propose temporal as product Mittag-Leffer functions adjacency matrices snapshots. then show that resolvent- and exponential-communicabilities are special cases new one when perfect (resolvent) or imperfect (exponential) considered By using theoretical empirical evidence real-world systems works out memory, trade off memory-dependent communication spatial transmission information. illustrate our results study trophallaxis interactions ant colonies.