  Social networks play a fundamental role in the diffusion of information.
However, there are two different ways of how information reaches a person in a
network. Information reaches us through connections in our social networks, as
well as through the influence of external out-of-network sources, like the
mainstream media. While most present models of information adoption in networks
assume information only passes from a node to node via the edges of the
underlying network, the recent availability of massive online social media data
allows us to study this process in more detail. We present a model in which
information can reach a node via the links of the social network or through the
influence of external sources. We then develop an efficient model parameter
fitting technique and apply the model to the emergence of URL mentions in the
Twitter network. Using a complete one month trace of Twitter we study how
information reaches the nodes of the network. We quantify the external
influences over time and describe how these influences affect the information
adoption. We discover that the information tends to "jump" across the network,
which can only be explained as an effect of an unobservable external influence
on the network. We find that only about 71% of the information volume in
Twitter can be attributed to network diffusion, and the remaining 29% is due to
external events and factors outside the network.
