This work reports a novel computational method based on augmented cell-graphs (ACG), which are constructed from low-magnification tissue images for the mathematical diagnosis of brain cancer (malignant glioma). An ACG is a simple, undirected, weighted and complete graph in which a node represents a cell cluster and an edge between a pair of nodes defines a binary relationship between them. Both the nodes and the edges of an ACG are assigned weights to capture more information about the topology of the tissue. In this work, the experiments are conducted on a dataset that is comprised of 646 human brain biopsy samples from 60 different patients. It is shown that the ACG approach yields sensitivity of 97.53% and specificities of 93.33 and 98.15% (for the inflamed and healthy, respectively) at the tissue level in glioma diagnosis.