Leveraging powerful planning and reasoning capabilities, Large Language Models (LLMs)-driven Multi-Agent Systems (MAS) have demonstrated remarkable scalability and generalizability across complex tasks. However, dynamically routing the optimal combination of agents and collaboration modes for a given query to balance performance and cost remains challenging. To address the limitation of prior work, which focuses on single-agent settings and overlooks collaborative structures and role assignment in MAS, we propose RouterHGC, the first heterogeneous graph contrastive learning framework for MAS routing. We formalize routing as node selection through edge-weight prediction on a heterogeneous graph whose node types include user queries, collaboration modes, agent roles, and LLMs, with message passing capturing their high-order dependencies. We further design a novel global–local contrastive loss function to jointly optimize graph-level representations and edge-level selections, pulling each query graph toward high-performing positives while pushing it away from underperforming or costly negatives. Experiments on five public datasets covering mathematical reasoning, code generation, and knowledge question answering show that RouterHGC outperforms the best single LLM and baselines, achieving 0.80%–6.17% accuracy gains on MATH and HotpotQA while reducing inference cost by 27.40%.