Graphs is an interesting topic as such. Even more, the concepts and algorithms used to tackle graph problems are elegant. Compiling a list of graph theory concepts would be a lot tedious but if your focus is on sport programming then I might make sense.
My pick would be:
0. The basics – graph notations, graph representations
1. graph traversal (BFS / DFS ) – perhaps the most versatile topic in graph theory. Just look at the applications of these methods, both have their own unique properties.
2. Shortest Path (Dijkstra / Bellman Ford / Floyd-Warshall)
3. Minimum spanning trees (Prim’s / Kruskal’s)
5. Lowest Common Ancestor (LCA algo : I, II, III, IV)
6. Min cut / Max Flow / Matching : topcoder
7. Strongly connected components : SCC
8. Articulation points and edges : Explanation of Algorithm for finding articulation points or cut vertices of a graph
Also there are some optimization techniques like Heavy light decomposition
These are the basics of graph to get on with graph questions.