A random graph model for terrorist transactions

We present a simple model for transactional evidence of terrorist activities that occur in the midst of massive amounts of "transactional noise". The theory is based on random graphs. We consider two random graph processes: an uncorrelated noise model G(n,p) and a target plus noise model G_H(n,p) that prescribes a threat subgraph H within the generated evidence graph. We derive a closed form expression for the likelihood ratio statistic that discriminates between the two processes. The results are extended to other random graph processes, including one in which some of the edges are not visible to the observer. The results suggest that pattern detection in structured, linked data requires pattern matching and that detection with imperfect observability requires hypotheses management.