Recent progress in natural language processing has popularized causal language models, but their internal behavior remains poorly understood due to the high cost and reliance on large-scale benchmarks in existing analysis methods. To address these challenges, we introduce a graph-theoretical framework for analyzing causal language models. Our method constructs graphs from model outputs by linking high-probability token transitions and applies classical metrics to capture linguistic features of model behavior. Based on previous works, none have examined or applied graph analysis from this perspective. For the first time, a macroscopic view of the overall behavior of a language model is provided by analyzing the mathematical characteristics of small sample graphs derived from the generated outputs. We first discuss the metrics theoretically, then demonstrate how they work through experiments, followed by some applications of this graph-theoretical framework in natural language processing tasks. Through experiments across training steps and model sizes, we demonstrate that these metrics can reflect model evolution and predict performance with minimal data. We further validate our findings by comparing them with benchmark accuracy scores, highlighting the reliability of our metrics. In contrast to existing evaluation methods, our approach is lightweight, efficient, and especially well-suited for low-resource settings.