The success of Federated Learning (FL) hinges upon the active participation and contributions of edge devices as they collaboratively train a global model while preserving data privacy. Understanding the behavior of individual clients within the FL framework is essential for enhancing model performance, ensuring system reliability, and protecting data privacy. However, analyzing client behavior poses a significant challenge due to the decentralized nature of FL, the variety of participating devices, and the complex interplay between client models throughout the training process. This research proposes a novel approach based on eccentricity analysis to address the challenges associated with understanding the different clients' behavior in the federation. We study how the eccentricity analysis can be applied to monitor the clients' behaviors through the training process by assessing the eccentricity metrics of clients' local models and clients' data representation in the global model. The Kendall ranking method is used for evaluating the correlations between the defined eccentricity metrics and the clients' benefit from the federation and influence on the federation, respectively. Our initial experiments on a publicly available data set demonstrate that the defined eccentricity measures can provide valuable information for monitoring the clients' behavior and eventually identify clients with deviating behavioral patterns. © 2024 IEEE.