I am using MySQL to store reports from a tool. I am extremely happy with the speed and flexibility with which users can query data. The tool also has some data which is a graph. My question is, is it a good idea to store the graph in MySQL? The number of nodes and edges in the graph is in the millions and queries are usually graph traversals.
MySQL is not created and optimized as a graph database in particular. You might want to try Neo4J which is a good graph database.
Plain SQL is usually unfit for manipulating a graph datastructure. There are techniques to index it, however.
For instance, if yours is not frequently updated, using a GRIPP index will let you handle graph traversal queries extremely well. The latter lets you answer parent-child and depth-related queries in more or less fixed time -- irrespective of the graph's number of nodes or density of links.