Networks describe systems in biology and beyond, from protein interactions and social relationships to power grids and citation records. Reasoning about such systems requires understanding their structure: which elements are central, which connections bridge separate communities, and how it changes when elements are removed. Although large language models (LLMs) excel at natural language, they struggle with such questions when networks are given as edge lists, sentences or measurement tables, because their structural meaning must be inferred. Here we introduce BioGlyph, which compiles network topology into an interpretable and transferable language of structural roles. BioGlyph combines graph partitioning and structural measurements to identify roles such as hubs, community cores and cross-community connectors, and fixed rules to translate them into a universal vocabulary. The representation describes each element through its structural role, supporting evidence and semantic consequences, leaving both the network and the LLM unchanged. Across twenty networks spanning five domains, BioGlyph substantially improves open LLMs' ability to answer structural reasoning questions, outperforming edge-based, numerical and learned representations by up to 26 percentage points in system accuracy. Ablations show that the gain comes from explicitly encoding structural roles in semantically interpretable terms. The gain is more prominent in dense, community-structured networks and diminishes in sparse networks whose topology is more readily inferred from text. In a budding-yeast protein-interaction network, BioGlyph exposes biological organization: cross-community connectors are enriched for essential genes, whereas peripheral proteins are depleted. BioGlyph thus provides an interpretable representation for both language models and scientists to reason about network structure.

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