We report a novel, proof-of-concept, computational method that models a type of brain cancer (glioma) only by using the topological properties of its cells in the tissue image. From low-magnification (80x) tissue images of 384 x 384 pixels, we construct the graphs of the cells based on the locations of the cells within the images. We generate such cell graphs of 1000-3000 cells (nodes) with 2000-10,000 links, each of which is calculated as a decaying exponential function of the Euclidean distance between every pair of cells in accordance with the Waxman model. At the cellular level, we compute the graph metrics of the cell graphs, including the degree, clustering coefficient, eccentricity and closeness for each cell. Working with a total of 285 tissue samples surgically removed from 12 different patients, we demonstrate that the self-organizing clusters of cancerous cells exhibit distinctive graph metrics that distinguish them from the healthy cells and the unhealthy inflamed cells at the cellular level with an accuracy of at least 85%. At the tissue level, we accomplish correct tissue classifications of cancerous, healthy and non-neoplastic inflamed tissue samples with an accuracy of 100% by requiring correct classification for the majority of the cells within the tissue sample.