Going out on a limb here because your question can be interpreted in multiple ways and I only feel qualified to answer one of them: The most common example for

Going out on a limb here because your question can be interpreted in multiple ways and I only feel qualified to answer one of them: The most common example for graphs in DBs would be a graph representing the friends/contacts of users. It's one of these "you'll know when you need it" solutions. Sometimes your data structure is a graph, and sometimes you want that graph to live in a database. And in even rarer cases you want to search that graph in your database in some recursive manner.