Why do you say that? -- see "MySQL vs. Neo4j on a Large-Scale Graph Traversal" (http://markorodriguez.com/2011/02/18/mysql-vs-neo4j-on-a-lar...).
You can represent a graph in almost any data structure, including a relational database. But the difference between a graph database and everything else is that in a real graph database (like Neo4j), each node has an internal/local index for its adjacent nodes so it doesn't have do an external look up for each traversal step.
Watch this video on "The Graph Traversal Programming Pattern" to see what I'm talking about (http://vimeo.com/13213184).