In recent years, several studies have shown that the cellular architecture of a tumour tissue, which may be highly unorganized and heterogeneous, has an important impact on drug delivery and treatment efficiency. The expanding field of digital histopathology, which is employing the latest advanced image analysis techniques, has now opened up a new dimension to investigate about the complexity of tumour tissue architecture and tumour micro-environment. Among the computational techniques and analytical tools used in digital pathology, graph-based methods have recently gained immense popularity as they can describe tissue architecture and provide useful information for spatial analysis. Graphs have the ability to characterize spatial arrangements and neighbourhood relationships of different tissue components like cell nuclei or glandular structures. One of the techniques that can be combined with graph theory to quantitatively analyse the topology of histological tissue is mathematical morphology (MM). We propose to study the dynamic of cell growth and tissue architecture with tools of MM on graphs. The morphological features that can be extracted from graphs using MM operations like erosion, dilation, opening and closing, have the potential to describe and characterize cell population growth considering their neighbourhood relationships.