Fanningfactor

Fanningfactor is a term used in the study of diffusion processes on networks to describe the breadth or fan-out of spread from an initial source. It is not tied to one universal definition, but it commonly serves as a dimensionless measure of how rapidly influence, information, or contagion propagates through a system.

One practical definition defines the fanningfactor F from a diffusion process as the average growth ratio of newly activated nodes in successive time steps. If A_t denotes the number of nodes activated at time t, then F can be estimated by F ≈ average of A_{t+1}/A_t over the active window. A related approach describes F as the mean branching factor across levels of the diffusion tree. In both forms, larger values indicate a more rapidly expanding spread, while values below one suggest damping.

Interpretation and usage: Fanningfactor provides a compact summary of diffusion dynamics and can help compare different networks, seeding strategies, or diffusion models. It is often used in information diffusion, viral marketing, and theoretical epidemiology to assess potential reach and to design interventions. Values of F can be sensitive to the chosen diffusion model (for example, independent cascade vs. threshold models), the seed node, and the network’s structure, so it is usually reported with context.

See also: diffusion on networks, branching process, Fano factor. Note that fanningfactor is a conceptual tool with multiple possible definitions, and users should specify the exact definition and calculation method in any application.