Extended Data Fig. 1: Comparison of composition-based clusters and microenvironment clusters.

A. and B. We generate composition-based clusters with cell type compositions of 3-hop subgraphs (microenvironments) following the same procedure. Note that the average predictions of microenvironment clusters are much more polarized. C. The composition cluster highly enriched with granulocytes has neutral average predictions/labels, it could be further dissected into multiple sub-clusters that belong to different microenvironment clusters. We see a pair of granulocyte/tumor microenvironments that have opposite outcome labels, see Results for further discussion. D. Similarly, the composition cluster enriched with vessel/lymph vessel cells could be dissected into multiple sub-clusters, from which we notice two microenvironment clusters that are both enriched with lymph vessel cells but have different composition and outcome predictions, see Supplementary Note 7 for further discussion. E. Comparison of the two microenvironments enriched in lymph vessel cells: the left column shows a microenvironment with more lymphocytes and has overall positive outcomes; the right column shows a contrasting group with more tumor cells and much worse outcome predictions. Observation of tumor cells in close vicinity of lymph vessels indicates potential lymphovascular invasion and will lead to worse prognosis, which aligns with model predictions.