Approximate Contagion Model of Common Knowledge on Facebook

Computational modeling of information exchange over social media is important for understanding coordination in online environments. Many contagion dynamics models that have been used to model Twitter, Facebook, and blog information transmission are polynomial-time computable, and hence can be efficiently simulated on networked populations. Game-theoretic models of collective action (i.e., coordination problems that require common knowledge among agents), however, have dynamics that are controlled in part by specific network structures such as cliques and bicliques. Contagion dynamics with these models cannot be efficiently computed because finding all bicliques in a graph, for example, is an NP-hard problem. We investigate a recent model of common knowledge dynamics that represents information spread on Facebook in which the biclique is the characterizing structure and convert the model into an efficiently computable one by using an approximation. We demonstrate this through experiments on seven different graphs for a total of 168 sets of conditions, including a 4-order of magnitude span in dynamics parameter values. Our approach speeds computations in two ways: (i) it obviates the need to find all bicliques in a social network, which is a very time- consuming task (computations can take 30 to 120 hours or more of wall clock time), and (ii) it reduces the time of simulation computations, in some cases by well over an order of magnitude. Our method also enables evaluation of much larger networks that are being mined from social media.