Advances in fusion of disparate social media and hard-soft sources have made it possible to extract relational information in the form of social network graphs. Periodic measurements of communication between individuals in an area of interest can be modeled in the form of a random graph. In this paper we are interested in detecting the emergence of a social network community where a subset of individuals of the dynamic random graph abruptly exhibits higher levels of communication (specifically, more ties among the members). An Erdös-Rényi random graph model is adopted. We employ a sequential change detection framework and propose a stopping rule to identify the emergence of a community with minimal expected detection delay while the probability of false alarms goes to zero asymptotically. We prove the optimality of this change detection rule and we compute its operating characteristics. We corroborate our results with simulation experiments. The practical contribution of our research is for alerting the formation of a community or terrorist group, for example.