Network Traces on Penetration: Uncovering Degree Distribution from Adoption Data

We show how networks modify the diffusion curve by affecting its symmetry. We demonstrate that a network's degree distribution has a significant impact on the contagion properties of the subsequent adoption process, and we propose a method for uncovering the degree distribution of the adopter network underlying the dissemination process, based exclusively on limited early-stage penetration data. In this paper we propose and empirically validate a unified network-based growth model that links network structure and penetration patterns. Specifically, using external sources of information, we confirm that each network degree distribution identified by the model matches the actual social network that is underlying the dissemination process. We also show empirically that the same method can be used to forecast adoption using an estimation of the degree distribution and the diffusion parameters at an early stage (15%) of the penetration process. We confirm that these forecasts are significantly superior to those of three benchmark models of diffusion. Our empirical analysis indicates that under heavily right-skewed degree distribution conditions (such as scale-free networks), the majority of adopters (in some cases, up to 75%) join the process after the sales peak. This strong asymmetry is a result of the unique interaction between the dissemination process and the degree distribution of its underlying network.