We investigate a bi-variate probabilistic model-building GA for the graph bipartitioning problem. The graph bipartitioning problem is a grouping problem that requires some modifications to the standard construction of the dependency tree. We also increase the computational efficiency of the Bi-PMBGA by restricting the dependency tree to the edges of the graph to be partitioned. Experimental results indicate that the Bi-PMBGA performs significantly better than the multi-start local search. Compared to a genetic local search algorithm the Bi-PMBGA performs slightly worse on some of the graphs considered here. Categories and Subject Descriptors I.2.8 [Problem Solving and Search]: General Terms Algorithms, Performance Keywords Probabilistic model-building EAs