To me, relational data is a graph, where each table is a node, and each foreign key is an edge connecting the two nodes together.
So when I hear about things like Neo4j and "graph databases", it is difficult for me to understand how they are inherently different from a relational model, which is already itself a graph!
Most important, because I can't tell the difference between the two, it's difficult for me to figure out which problem domains are best solved with a graph model, and which ones are best solved with a relational model. I'm looking for a set of guidelines to say: Hey, this problem is definitely best represented by a graph model, so I will use (say) Neo4j. Or, to say: This problem is definitely best represented by a relational model, so I will use (say) MySQL.
Edit: In summary, what problem domains (data-wise) do graph models solve better than relational models?