Information Flow in Networks — Trendsetters, Bellwethers and Shepherd Dogs

The rapid expansion of “social network research” is an exciting and unique phenomenon taking place in the last decade. Networks, from their essential definition, serve as an infrastructure for communication — either explicit (e.g. phone calls or emails), implicit (e.g. social signals), or a combination thereof (e.g. online social service such as Facebook or Flicker). As such, a fundamental aspect that must be addressed in order to truly comprehend networks, is the particular way they interact with and influence information that flows through them. Specifically, when addressing this issue, our goals should be threefold. First, we must aspire for the understanding the underlying mechanisms that control information flow in networks. This should be done by developing analytic models that describe the properties (both local and global) of this process. Second, using these models (or other methods that will be developed based on them) to generate predictions concerning the evolution of information propagation processes. This may include for example the ability to predict the probability that some trend or idea will epidemically spread throughout a given network, . Another example would be the assessment of the openness of networks to the proliferation and assimilation of new information or knowledge that are introduced to them by some of their members. Third, we are interested in developing techniques for efficiently intervening in this process. For example, such intervention may take the form of external stimuli that may be injected to the system in order to generate (or strengthen) certain social links, and subsequently facilitate the assimilation of future information that would be introduced to the network (i.e. the creation of “Shepherd dogs”, that increase the cohesion of the network). Alternatively, by efficiently recognizing the implicit “roles” of members of the network, certain members can be engaged (e.g. by informative or monetary means) in a way that influence the global behavior of the entire network (i.e. “Bellwethers” and “Trendsetters”). In order to formally discuss the ability of a new idea or a new piece of information to gain popularity over a network, we formally define two terms : “appeal factor” and “persistence factor”, denoting an idea’s local spreading and deletion expected probabilities, respectively. Using these terms we show that the ability of an idea to epidemically spread throughout a network can be analytically