In this paper we study how the network of agents adopting a particulartechnology relates to the structure of the underlying network over which thetechnology adoption spreads. We develop a model and show that the network ofagents adopting a particular technology may have characteristics that differsignificantly from the social network of agents over which the technologyspreads. For example, the network induced by a cascade may have a heavy-taileddegree distribution even if the original network does not. This provides evidence that online social networks created by technologyadoption over an underlying social network may look fundamentally differentfrom social networks and indicates that using data from many online socialnetworks may mislead us if we try to use it to directly infer the structure ofsocial networks. Our results provide an alternate explanation for certainproperties repeatedly observed in data sets, for example: heavy-tailed degreedistribution, network densification, shrinking diameter, and network communityprofile. These properties could be caused by a sort of `sampling bias' ratherthan by attributes of the underlying social structure. By generating networksusing cascades over traditional network models that do not themselves containthese properties, we can nevertheless reliably produce networks that containall these properties. An opportunity for interesting future research is developing new methods thatcorrectly infer underlying network structure from data about a network that isgenerated via a cascade spread over the underlying network.
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