Social media text summarization aims to provide concise summaries for large-scale social media short texts (referred to as posts) targeting specific topics. Given the brief and informal contents of posts, traditional methods confront the challenges of sparse features and insufficient information. Recent research endeavors have leveraged social relationships among posts to refine post contents and remove redundant information, but these efforts neglect the presence of unreliable noise relationships in real social media contexts, leading to erroneous assessments of post importance and diversity. Therefore, this study proposes a novel unsupervised model DSNSum, which improves summarization performance by removing noise relationships in the social networks. Firstly, the noise relationships in real social relationship networks are statistically verified. Secondly, two noise functions are designed based on sociological theories, and a denoising graph auto-encoder (DGAE) is constructed to mitigate the influence of noise relationships and cultivate post contents of credible social relationships. Finally, a sparse reconstruction framework is utilized to select posts that maintain coverage, importance, and diversity to form a summary of a certain length. Experimental results on a total of 22 topics from two real social media platforms (Twitter and Sina Weibo) demonstrate the efficacy of the proposed model and provide new insights for subsequent research in related fields.