  The urban-rural divide is increasing in modern societies calling for
geographical extensions of social influence modelling. Improved understanding
of innovation diffusion across locations and through social connections can
provide us with new insights into the spread of information, technological
progress and economic development. In this work, we analyze the spatial
adoption dynamics of iWiW, an Online Social Network (OSN) in Hungary and
uncover empirical features about the spatial adoption in social networks.
During its entire life cycle from 2002 to 2012, iWiW reached up to 300 million
friendship ties of 3 million users. We find that the number of adopters as a
function of town population follows a scaling law that reveals a strongly
concentrated early adoption in large towns and a less concentrated late
adoption. We also discover a strengthening distance decay of spread over the
life-cycle indicating high fraction of distant diffusion in early stages but
the dominance of local diffusion in late stages. The spreading process is
modelled within the Bass diffusion framework that enables us to compare the
differential equation version with an agent-based version of the model run on
the empirical network. Although both models can capture the macro trend of
adoption, they have limited capacity to describe the observed trends of urban
scaling and distance decay. We find, however that incorporating adoption
thresholds, defined by the fraction of social connections that adopt a
technology before the individual adopts, improves the network model fit to the
urban scaling of early adopters. Controlling for the threshold distribution
enables us to eliminate the bias induced by local network structure on
predicting local adoption peaks. Finally, we show that geographical features
such as distance from the innovation origin and town size influence prediction
of adoption peak at local scales.
