All common graph operations and more are built into Mathematica 8. This Demonstration lets you choose two graphs and the operation to apply to them. The graph union of two graphs and is the graph whose vertices and edges are the union of the corresponding vertices and edges of and . Sometimes we want to see and as two disjoint structures that are to be put together to form a bigger one; then we use the disjoint union. The difference is obtained by joining their vertices and deleting the edges of from the edges of . The intersection is the graph obtained by joining the vertices and intersecting the edges.