Social media offers an essential platform for individuals with depression to engage in self-disclosure, providing a safe and anonymous environment for expressing emotions and seeking support. However, societal prejudices and emotional barriers continue to hinder some users from fully disclosing their thoughts and feelings online. This study proposes a novel framework that integrates large language models (LLMs) and social network analysis to analyze behavioral characteristics of self-disclosure among online users with depression and investigate the multi-dimensional impact of social network support on these behaviors. An empirical study was conducted using data from an online depression community, where a social network consisting of 789 users (generating 441,966 post texts) and 4483 undirected edges was constructed. LLM was employed to analyze self-disclosure across three dimensions: themes of self-disclosure (personal information, health conditions, medical knowledge, and life activities), emotional expression in self-disclosure, and depth of self-disclosure. The auto-logistic actor attribute model (ALAAM) was then employed to analyze the impact of the social support network on self-disclosure. Results show that the presence of social network significantly encourages self-disclosure, yet an increase in social connections can paradoxically reduce such behavior. Self-disclosure exhibits a contagious effect, while gender and health literacy show no significant impact. However, higher online popularity negatively affects self-disclosure, and both positive and negative emotions positively influence this behavior. The findings enhance theoretical understanding of self-disclosure in depression through the use of LLMs and social network analysis and provide practical insights for optimizing online interventions and psychological support mechanisms.