Graph pattern matching is a fundamental operation for the analysis and exploration ofdata graphs. In thispaper, we presenta novel approachfor efficiently finding homomorphic matches for hybrid graph patterns, where each pattern edge may be mapped either to an edge or to a path in the input data, thus allowing for higher expressiveness and flexibility in query formulation. A key component of our approach is a lightweight index structure that leverages graph simulation to compactly encode the query answer search space. The index can be built on-the-fly during query execution and does not have to be persisted to disk. Using the index, we design a multi-way join algorithm to enumerate query solutions without generating any potentially exploding intermediate results. We demonstrate through extensive experiments that our approach can efficiently evaluate a wide range / broad spectrum of graph pattern queries and greatly outperforms existing approaches and recent graph query engines/systems.