While a multi-agent approach based on large language models (LLMs) represents a promising strategy to surpass the capabilities of single models, its success is critically dependent on synergistic team composition. However, forming optimal teams is a significant challenge, as the inherent opacity of most models obscures the internal characteristics necessary for effective collaboration. In this paper, we propose an interaction-centric framework for automatic team composition that does not require any prior knowledge including their internal architectures, training data, or task performances. Our method constructs a "language model graph" that maps relationships between models from the semantic coherence of pairwise conversations, and then applies community detection to identify synergistic model clusters. Our experiments with diverse LLMs demonstrate that the proposed method discovers functionally coherent groups that reflect their latent specializations. Priming conversations with specific topics identified synergistic teams which outperform random baselines on downstream benchmarks and achieve comparable accuracy to that of manually-curated teams based on known model specializations. Our findings provide a new basis for the automated design of collaborative multi-agent LLM teams.