Local community detection is a specialized area within the broader field of community detection, focusing on the identification of communities centered around a set of initial seed nodes. Despite increasing research interest over the past two decades, a comprehensive assessment of the diverse existing methods and their performance under varying conditions remains challenging. In this paper, we conduct a focused comparative study of several well-known local community detection algorithms, applied specifically to static undirected graphs. We implement representative algorithms and evaluate their behavior, strengths, and limitations across standard benchmark datasets. Our aim is to provide clear empirical insights into the performance and trade-offs of these algorithms, thereby guiding researchers in selecting appropriate methods for their use cases. We also present implementation details and evaluation results to promote reproducibility and facilitate further investigation.