What is a graph database?
A graph database is one that stores data in terms of entities and the relationships between entities. A variant on this theme are RDF (resource description framework) databases which store data in the format subject-predicate-object, which is known as a triple.
There are three types of graph database: true graph databases, triple stores and conventional databases that provide some graphical capabilities. Triple stores are often referred to as RDF databases. The difference between a true graph product and a triple store is that the former supports index free adjacency (which means you can traverse a graph without needing an index) and the latter doesn't. The former are designed to support property graphs (graphs where properties may be assigned to either entities or their relationships, or both) but recently some triple stores have added this capability.