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MOTIVATION: Knowledge graphs (KGs), collectively as a knowledge network, have become critical tools for knowledge discovery in computable and explainable knowledge systems. Due to the semantic and structural complexities of biomedical data, these KGs need to enable dynamic reasoning over large evolving graphs and support fit-for-purpose abstraction. Crucially, this requires establishing standards, preserving provenance and enforcing policy constraints for actionable discovery.RESULTS: A recent meeting of leading scientists discussed the opportunities, challenges, and future directions of a biomedical knowledge network. Here we present six desiderata inspired by the meeting: (i) inference and reasoning in biomedical KGs need domain-centric approaches, (ii) harmonized and accessible standards are required for knowledge graph representation and metadata, (iii) robust validation of biomedical KGs needs multilayered, context-aware approaches that are both rigorous and scalable, (iv) the evolving and synergistic relationship between KGs and large language models is essential in empowering AI-driven biomedical discovery, (v) integrated development environments, public repositories, and governance frameworks are essential for secure and reproducible knowledge graph sharing, and (vi) robust validation, provenance, and ethical governance are critical for trustworthy biomedical KGs. Addressing these key issues will be essential to realize the promises of a biomedical knowledge network in advancing biomedicine.