Graph Databases are good for storing relationships between two things where the relationships are at least as important as the items themselves. Graph Database are very good at analyzing how things are related ,How many steps are required to get from one point to other. Analyzing relationships between people in social media are typical use case of graph databases.
Sometimes the entities in the analysis are not known for example the real person behing the twitt on twitter or a post on Facebook but the relationships may be more important toward identifying groups that interact or how central an individual is to a group
Semantic analysis, or trying to understand the meaning of things, favors graph database solutions. Graph databases are frequently implemented using the triple store concept of object,predicate, and relationship, a basic concept in semantic analysis.