Self-play reinforcement learning has shown strong performance in domains with formally verifiable structure, such as mathematics and coding, where both problem generation and reward computation can be grounded in explicit rules. Extending this paradigm to scientific literature is more challenging: the relationships among multi-modal elements within and across documents are rarely made explicit in text, which makes automatic generation of relational reasoning questions difficult and weakens the reliability of reward signals. We propose SPARK (Self-Play with Asymmetric Reward from Knowledge Graphs), a framework that automatically constructs a unified knowledge graph (KG) from multi-document scientific literature and uses it as the structural basis for self-play. KG paths over multimodal nodes serve as a source for generating relational reasoning questions, and structured facts stored in the KG provide a basis for verifiable reward computation. A single small vision-language model (sVLM) alternates between Proposer and Solver roles under information asymmetry against a fixed KG, a design that we believe can be naturally extended toward online adaptation in future work. We evaluate SPARK on public benchmarks and a self-constructed cross-document multi-hop QA dataset. Results show that SPARK consistently outperforms flat-corpus-based self-play baselines, and the performance gap widens as hop count increases, suggesting that KG-structure grounding contributes to relational multi-hop reasoning beyond what unstructured corpus grounding can provide.