In today's business environment, competition within industries is becoming more and more intense. To survive in this fast-paced competitive environment, it's 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 (that is, core patents) and clusters (that is, patent groups) in a patent citation network simultaneously rather than separately. The method allows 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.