Potential networks, contagious communities, and understanding social network structure

In this paper we study how the network of agents adopting a particular technology relates to the structure of the under-lying network over which the technology adoption spreads. We develop a model and show that the network of agents adopting a particular technology may have characteristics that differ significantly from the social network of agents over which the technology spreads. For example, the net-work induced by a cascade may have a heavy-tailed degree distribution even if the original network does not. This provides evidence that online social networks created by technology adoption over an underlying social network may look fundamentally different from social networks and indicates that using data from many online social networks may mislead us if we try to use it to directly infer the struc-ture of social networks. Our results provide an alternate ex-planation for certain properties repeatedly observed in data sets, for example: heavy-tailed degree distribution, network densification, shrinking diameter, and network community profile. These properties could be caused by a sort of sam-pling bias rather than by attributes of the underlying social structure. By generating networks using cascades over tradi-tional network models that do not themselves contain these properties, we can nevertheless reliably produce networks that contain all these properties. An opportunity for interesting future research is devel-oping new methods that correctly infer underlying network structure from data about a network that is generated via a cascade spread over the underlying network