Inferring Network Structure from Cascades
  Many physical, biological, and social phenomena can be described by cascades taking place on a network. Often, the activity can be empirically observed, but not the underlying network of interactions. In this paper we offer three topological methods to infer the structure of any directed network given a set of cascade arrival times. Our formulas hold for a very general class of models where the activation probability of a node is a generic function of its degree and the number of its active neighbors. We report high success rates for synthetic and real networks, for several different cascade models. 
Sushrut Ghonge, Dervis Can Vural
cs.SI cond-mat.dis-nn physics.soc-ph