Graph database users today face a choice between two technology stacks: the Resource Description Framework (RDF), on one side, is a data model with built-in semantics that was originally developed by the W3C to exchange interconnected data on the Web; on the other side, Labeled Property Graphs (LPGs) are geared towards efficient graph processing and have strong roots in developer and engineering communities. The two models look at graphs from different abstraction layers (triples in RDF vs. edges connecting vertices with inlined properties in LPGs), expose - at least at the surface - distinct features, come with different query languages, and are embedded into their own software ecosystems. In this short paper, we introduce a novel unifying graph data model called Statement Graphs, which combines the traits of both RDF and LPG and achieves interoperability at different levels: it (a) provides the ability to manage RDF and LPG data as a single, interconnected graph, (b) supports querying over the integrated graph using any RDF or LPG query language, while (c) clearing the way for graph stack independent data exchange mechanisms and formats. We formalize our new model as directed acyclic graphs and sketch a system of bidirectional mappings between RDF, LPGs, and Statement Graphs. Our mappings implicitly define read query semantics for RDF and LPGs query languages over the unified data model, thus providing graph users with the flexibility to use the query language of their choice for their graph use cases. As a proof of concept for our ideas, we also present the 1G Playground; an in-memory DBMS built on the concepts of Statement Graphs, which facilitates storage of both RDF and LPG data, and allows for cross-model querying using both SPARQL and Gremlin.