Check out JGraphT for a very simple and powerful Java graph library that is pretty well done and, to allay any confusion, is different than JGraph. Some sample code:
UndirectedGraph g =
new SimpleGraph(DefaultEdge.class);
String v1 = "v1";
String v2 = "v2";
String v3 = "v3";
String v4 = "v4";
// add the vertices
g.addVertex(v1);
g.addVertex(v2);
g.addVertex(v3);
g.addVertex(v4);
// add edges to create a circuit
g.addEdge(v1, v2);
g.addEdge(v2, v3);
g.addEdge(v3, v4);
g.addEdge(v4, v1);