Here we develop we develop a novel Geometry Interaction Learning (GIL) method for graphs, a well-suited and efficient alternative for learning complex geometric properties real-world graphs. Our method endows each node the freedom to determine the importance of each geometry space via a flexible dual feature interaction learning and probability assembling mechanism. Furthermore, our method endows each node the freedom to determine the importance of each geometry space via a flexible dual feature interaction learning and probability assembling mechanism. Promising experimental results are presented for five benchmark datasets on node classification and link prediction tasks.