The role of geography in the complex diffusion of innovations

The urban-rural divide is increasing in modern societies and is influencing economic and social inequality, and political radicalization. These observed trends are deeply rooted in the spatial patterns of society, and require geographical extensions in network models of social influence. improved understanding of the ways in which new technologies and new ideas diffuse across locations can provide us with new insights into the spread of information, technological progress and economic development. In this work, we uncover the role of geography in the spatial diffusion of innovations via a unique dataset from iWiW, which is an online social network (OSN) in Hungary. We analyze its entire life cycle from 2002 to 2012, reaching up to 300 million friendships at the peak of its popularity and the subsequent disappearance after its failed competition with international OSN platforms. By applying a complex diffusion model on the empirical spatial social network, we observe that the connections of individuals with similar tendency to adopt, or assortative mixing, is crucial in spatial spreading. However, predicting the likelihood of adoption is the aim of diffusion models and a priori labeling of individuals in these models would be a paradox. Alternatively, we reveal the scaling laws in the number of innovators and early adopters in towns as a function of their population and gravity laws on the distance of ties. These empirical features need to be included in models of complex contagion.