Brain MRI segmentation remains a challenging problem in spite of numerous existing techniques. To overcome the inherent difficulties associated with this segmentation problem, we present a new method of information integration in a graph based framework. In addition to image intensity, tissue priors and local boundary information are integrated into the edge weight metrics in the graph. Furthermore, inhomogeneity correction is incorporated by adaptively adjusting the edge weights according to the intermediate inhomogeneity estimation. In the validation experiments of simulated brain MRIs, the proposed method outperformed a segmentation method based on iterated conditional modes (ICM), which is a commonly used optimization method in medical image segmentation. In the experiments of real neonatal brain MRIs, the results of the proposed method have good overlap with the manual segmentations by human experts.