In today's business environment, competition within the industries is becoming more and more intense. In order to survive in this fast paced competitive environment, it is important to know what the competitive technology is and how the technologies can be grouped. Therefore, this study focuses on discovering the core technology and clustering technologies simultaneously using patent citation network where the core technology is represented as an influential node and the technology group as a cluster of nodes. However, existing methods have discovered the influential nodes and cluster nodes separately, especially in a citation network. This article develops the method to detect the influential nodes and clusters simultaneously in a patent citation network. It can allow an important patent in each patent group to be discovered easily and the distribution of the similar patents around the important patent to be recognized. For the study of detecting important patents and their groups simultaneously, kernel k-means clustering method with graph kernel is introduced. A graph kernel helps to compute implicitly similarities between patents in a high-dimensional feature space, even if the similarities between structured patents cannot be explicitly represented. The proposed approaches are compared to the widely used centrality measures using US patents data in the area of information and security.