Authors:
Balazs Lengyel | Massachusetts Institute of Technology | United States
Riccardo Di Clemente | United States
János Kertész | Hungary
Marta C. González | United States
Social networks have been extensively used to study how innovative ideas, products or services spread through society. However, it is not fully understood how social contagion happens in space, how diffusion takes place over the life-cycle of products, and how churning happens in spatial social networks. In this paper, we use a unique dataset compiled from a Hungarian online social network (OSN) that was established earlier than international OSNs and was closed down after failing the competition with Facebook [1]. We find that the OSN was adopted early in large towns where churning also happened early. However, while the coefficient of imitation in the Bass DE diffusion model varies, the rate of exponential growth in churning is surprisingly stable across towns. Using information on invitations to register on the OSN, we show that the extent of town-level transmission became a superlinear function of town size by the middle of the product life-cycle. Interestingly, invitations became less and less likely to be sent to large distances; we find that the exponent of the distance decay function increases over the life-cycle. Further, we discover that the cascade of churn is local because the fraction of proximate friends who already churned is smaller than the fraction of distant friends who already churned when the user in focus decides to churn [2]. Finally, we develop an agent-based Bass model of diffusion on the one hand and an agent-based threshold model of churn on the other hand. With these models we target town-level peaks of adoption and town-level critical mass of churn, respectively, in order to exploit how geographical distance influences diffusion and churning processes in social networks.
[1] Lengyel B, Varga A, Ságvári B, Jakobi Á, Kertész, J (2015) Geographies of an online social network. PLoS ONE 10(9): e0137248.
[2] Centola D, Macy M (2007) Complex contagions and the weakness of long ties. American Journal of Sociology 113(3): 702-734.