Innovation diffusion equations on correlated scale-free networks

TL;DR

This paper extends the Bass diffusion model to correlated scale-free networks, analyzing how innovation spreads with heterogeneous structures and processes, including trickle-up dynamics and stochastic effects, demonstrating the model's robustness.

Contribution

It introduces a novel network-structured diffusion model incorporating heterogeneity, stochasticity, and trickle-up processes, expanding the applicability of the Bass model.

Findings

Hubs' adoption anticipates total adoption in trickle-down processes.

Heterogeneous publicity coefficients can turn hubs into stiflers.

The model remains robust under various network and process modifications.

Abstract

We introduce a heterogeneous network structure into the Bass diffusion model, in order to study the diffusion times of innovation or information in networks with a scale-free structure, typical of regions where diffusion is sensitive to geographic and logistic influences (like for instance Alpine regions). We consider both the diffusion peak times of the total population and of the link classes. In the familiar trickle-down processes the adoption curve of the hubs is found to anticipate the total adoption in a predictable way. In a major departure from the standard model, we model a trickle-up process by introducing heterogeneous publicity coefficients (which can also be negative for the hubs, thus turning them into stiflers) and a stochastic term which represents the erratic generation of innovation at the periphery of the network. The results confirm the robustness of the Bass model and expand considerably its range of applicability.