The role of geography in the complex diffusion of innovations
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 model versions 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 in all model
specifications.