Figure 3. Graphs of differing symmetry.

Graph 1 is a complete graph with all nodes connected; it has 6 rotation and 12 reflection symmetries. Graph 2 is the smallest asymmetric graph. Graph 3 is the smallest asymmetric graph with each node possessing 3 edges (degree 3); it is known as the Frucht graph. Graph 4 is a complex graph, such as might exist for interacting proteins, for which any imbedded symmetries are difficult to discern by inspection. Software programs, such as nauty and SAUCY2, can compute the graph automorphisms.