Neo4j API offers methods for graph traversal out-of-the-box which are likely the same ones that most people will use.
Interestingly, Marko didn't use Neo4j's native API (http://api.neo4j.org) -- he used a dataflow framework he wrote called Pipes (https://github.com/tinkerpop/pipes/wiki/).
You probably have heard of the graph programming language Gremlin (https://github.com/tinkerpop/gremlin/wiki). Gremlin is a thin wrapper over Pipes.