The analysis of conversational dynamics has gained increasing importance with the rise of large language model-based systems, which interact with users across diverse contexts. In this work, we propose a novel computational framework for constructing conversational graphs that capture the flow and structure of loosely organized dialogues, referred to as quasi-patterned conversations. We introduce the Filter & Reconnect method, a novel graph simplification technique that minimizes noise while preserving semantic coherence and structural integrity of conversational graphs. Through comparative analysis, we demonstrate that the use of large language models combined with our graph simplification technique has resulted in semantic metric S increasing by a factor of 2.06 compared to previous approaches while simultaneously enforcing a tree-like structure with 0 δ-hyperbolicity, ensuring optimal clarity in conversation modeling. This work provides a computational method for analyzing large-scale dialogue datasets, with practical applications related to monitoring automated systems such as chatbots, dialogue management tools, and user behavior analytics.