Detecting subgraphs of interest in larger graphs is the goal of many graph analysis techniques. The basis of detection theory is computing the probability of a “foreground” with respect to a model of the “background” data. Hidden Markov Models represent one possible foreground model for patterns of interaction in a graph. Likewise, Kronecker graphs are one possible model for power law background graphs. Combining these models allows estimates of the signal to noise ratio, probability of detection, and probability of false alarm for different classes of vertices in the foreground. These estimates can then be used to construct filters for computing the probability that a background graph contains a particular foreground graph. This approach is applied to the problem of detecting a partially labeled tree graph in a power law background graph. One feature of this method is the ability to a priori estimate the number of vertices that will be detected via the filter.