Small language models (SLMs) are increasingly paired with knowledge graphs (KGs), yet end-to-end KG question answering conflates graph access, search, navigation, reasoning, and answer generation. This coupling makes it difficult both to determine whether an SLM can faithfully execute the reasoning path implied by a question and to attribute failures to navigation rather than to other stages of the pipeline. We isolate this capability by employing the THESEUS navigation and traceability framework and using frozen, off-the-shelf SLMs as local action policies. At each hop, the environment exposes the legal outgoing graph actions, and the model selects one executable graph action and decides whether to stop, without task-specific parameter updates, model-controlled beam search, or free-form answer generation. This controlled setting allows us to evaluate terminal-answer accuracy with Hits@1 together with path fidelity, using Path Edit Distance (PED) as the primary trajectory metric. Across the Kinship and MQuAKE-ST KGQAs, similarly sized local models differ substantially in answer accuracy and path fidelity, with the two metrics sometimes favoring different models. This model-dependent behavior also extends to prompting, as a single demonstrated trajectory can improve or degrade navigation depending on the model. These results motivate evaluating SLM graph reasoning beyond endpoint accuracy alone.
LLM-based knowledge-graph question answering (KGQA) delegates graph traversal to language models, turning each question into a sequence of local relation-selection decisions repeated across beams and hops. A common but untested default is to serialize the complete partial path into every routing prompt, even though the controller already maintains this path as exact symbolic state. Bounded Path Context (BPC) decouples these two roles: the controller retains full paths in symbolic memory for answer extraction and audit, while the relation-selection prompt exposes only the question, the current entity, outgoing relation candidates, and at most the last K hops. A controlled sweep over K -- fixing graph neighborhoods, beam budget, depth, decoding, and answer-extraction format -- shows that bounded histories match or exceed full-history prompting on complete WebQSP and CWQ test sets with Qwen3.5-9B-AWQ: K=1 achieves 0.487 answer-set F1 on WebQSP versus 0.472 for full history, and K=0 reaches 0.287 on CWQ versus 0.274, with 9.7% and 12.1% fewer input tokens respectively. At the 4B scale, K=1 remains the strongest setting on both benchmarks. Per-example analysis reveals that 71-84% of examples are unaffected by history length, while the affected cases expose when prior hops disambiguate versus distract. These results suggest that path serialization length is better treated as a tunable interface variable than as a default assumption in LLM-based graph controllers.
Knowledge graph question answering (KGQA) requires navigating from topic entities to an answer several relations away. Recent methods prompt a frontier LLM to explore the graph through a retrieval tool, but their reliance on frontier-scale inference makes them costly to deploy. We present Search-on-Graph-R1 (\sogrone{}), which internalizes this navigation into a compact 8B model through supervised fine-tuning (SFT) followed by reinforcement learning (RL). Our central idea is to scaffold a frontier teacher with each question's gold SPARQL query, so the teacher traverses a known answer-bearing path with a live \texttt{Search} tool rather than having to discover the path itself. Since every call executes against a live Freebase server, the resulting trajectories are grounded in the knowledge graph by construction. On WebQSP, CWQ, and GrailQA, \sogrone{} at 8B surpasses every frozen frontier-LLM system in our comparison and posts the strongest results on CWQ of any system we compare against. It does so using no auxiliary module at inference and no LLM judge during training. Isolating each training stage shows that SFT and RL contribute complementary gains, our approach transfers across model families, and RL learns to reach answers in fewer \texttt{Search} calls than its SFT initialization.
A graph retrieval-augmented generation pipeline chooses which triples to put in the prompt, a syntax to write them in, an order to write them in, and a sentence telling the model what to do with them. We vary all four over six large language models and two knowledge-graph question answering benchmarks. Two of the four choices move the answer and the other two are flat. The first is whether the answer path, the triples needed to reach the answer, is in the prompt at all. Holding the number of triples fixed and replacing every triple that is not on the chain with material from an unrelated entity changes answer accuracy by +0.003 F1, while removing the chain costs most of what the graph was worth. Retrieval budget belongs on recall, and precision in the range we can test buys nothing. There is no retriever here: subgraphs come from gold SPARQL, so precision describes the context we build, not a system setting. The second is the grounding instruction. With no facts in the prompt, telling a model to answer using only the provided facts drops F1 from 0.299 to 0.035, a factor of 8.63. That figure describes an evaluation with an empty context arm rather than a working pipeline, and an experiment that applies the instruction to its context arm but not to its no-context baseline manufactures a spurious finding that graph context hurts at depth. We found one in our own results and retract it. Syntax, triple order and subgraph size produce no effect we can measure at multi-hop depth. The comparison that would price the grounding instruction against correct context is not measurable with a format-sensitive scorer, because the instruction determines the response format; we report it as an open contrast rather than a number.