The PDZ domain of proteins mediates a protein-protein interaction by recognizing the hydrophobic C-terminal tail of the target protein. One of the challenges put forth by the DREAM (Discussions on Reverse Engineering Assessment and Methods) 2009 Challenge consists of predicting a position weight matrix (PWM) that describes the specificity profile of five PDZ domains to their target peptides. We consider the primary structures of each of the five PDZ domains as a numerical sequence derived from graph-theoretic models of each of the individual amino acids in the protein sequence. Using available PDZ domain databases to obtain known targets, the graph-theoretic based numerical sequences are then used to train a neural network to recognize their targets. Given the challenge sequences, the target probabilities are computed and a corresponding position weight matrix is derived. In this work we present our method. The results of our method placed second in the DREAM 2009 challenge.