In today’s business environment, competition within industries is becoming more and more intense. To survive in this fast-paced competitive environment, it is important to know what the core patents are and how the patents can be grouped. This study focuses on discovering core patents and clustering patents using a patent citation network in which core patents are represented as an influential node and patent groups as a cluster of nodes. Existing methods have discovered influential nodes and cluster nodes separately, especially in a citation network. This study develops a method used to detect influential nodes (i.e., core patents) and clusters (i.e., patent groups) in a patent citation network simultaneously rather than separately. It can allow a core patent in each patent group to be discovered easily and the distribution of similar patents around a core patent to be recognized. For this study, kernel k-means clustering with a graph kernel is introduced. A graph kernel helps to compute implicit similarities between patents in a high-dimensional feature space.