Semi-Supervised Graph Clustering (SSGC) has emerged as a pivotal field at the intersection of graph clustering and semi-supervised learning (SSL), offering innovative solutions to intricate data analysis problems. However, despite its significance and wide-ranging applications, there exists a notable void in the literature—a comprehensive survey specifically dedicated to SSGC techniques and their diverse applications remains conspicuously absent. Addressing this gap, this paper presents a systematic and comprehensive review of SSGC methodologies, spanning from well-established approaches to cutting-edge developments. Through a meticulous categorization, critical examination, and insightful discussion of these techniques, this survey not only illuminates the current landscape of SSGC but also identifies unexplored avenues for exploration and innovation. In this paper we present a comprehensive survey of conventional graph construction, graph clustering, SSL methods, evaluation metrics and their primary development process. We then provide a taxonomy of SSGC techniques based on their structures and principles and thoroughly analyze and discuss the related models. Furthermore, we review the applications of SSGC in various fields. Lastly, we summarize the limitations of current SSGC algorithms and discuss the future directions of the field.
