The rapid diffusion of information and the fragmentation of discourse across diverse social media platforms pose significant public health and societal challenges. To understand these complex online ecosystems, we present our recent research frameworks, highlighting our contributions in three folds. First, we explore narrative analysis using an LLM-enhanced knowledge graph to systematically map and evaluate complex storylines. Second, we demonstrate social network analysis using knowledge graphs applied to multiple topics, such as public health and hate speech, and across multiple platforms to reveal structural and semantic community dynamics. Third, we present spectral analysis on the knowledge graph, utilizing diffusion-based metrics to uncover latent structural pathways for robust misinformation detection. This work is supported by the National Science Foundation.