This document discusses integrating graph processing capabilities into relational database management systems (RDBMS). It proposes GRAPHITE, a native graph engine with graph operators that can be combined with other relational operators. GRAPHITE stores graphs columnarly and includes graph traversal operators like fragmented-incremental traversal. It also introduces TraveL, a domain-specific language for writing graph traversals, which can be compiled into execution plans. Initial experimental results on breadth-first search traversals and LDBC Query 1 are provided.