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This work presents a graph-based representation (a.k.a., cell-graph) of histopathological images for automated cancer diagnosis by probabilistically assigning a link between a pair of cells (or cell clusters). Since the node set of a cell-graph can include a cluster of cells as well as individual ones, it enables working with low-cost, low-magnification photomicrographs. The contributions of this work are twofold. First, it is shown that without establishing a pairwise spatial relation between the cells (i.e., the edges of a cell-graph), neither the spatial distribution of the cells nor the texture analysis of the images yields accurate results for tissue level diagnosis of brain cancer called malignant glioma. Second, this work defines a set of global metrics by processing the entire cell-graph to capture tissue level information coded into the histopathological images. In this work, the results are obtained on the photomicrographs of 646 archival brain biopsy samples of 60 different patients. It is shown that the global metrics of cell-graphs distinguish cancerous tissues from noncancerous ones with high accuracy (at least 99 percent accuracy for healthy tissues with lower cellular density level, and at least 92 percent accuracy for benign tissues with similar high cellular density level such as nonneoplastic reactive/inflammatory conditions).