This paper reports a new structural method to mathematically represent and quantify a tissue for the purpose of automated and objective cancer diagnosis and grading. Unlike the previous structural methods, which quantify a tissue considering the spatial distributions of its cell nuclei, the proposed method relies on the use of distributions of multiple tissue components for the representation. To this end, it constructs a graph on multiple tissue components and colors its edges depending on the component types of their endpoints. Subsequently, it extracts a new set of structural features from these color graphs and uses these features in the classification of tissues. Working with the images of colon tissues, our experiments demonstrate that the color-graph approach leads to 82.65% test accuracy and that it significantly improves the performance of its counterparts.