Centrality measures such as degree centrality have been utilized to identify influential and important patents in a citation network. However, no existing centrality measures take into consideration information from the change of the similarity matrix. This paper presents a new centrality measure based on the change of a node similarity matrix. The proposed approach gives more intuitive understanding of the finding of the influential nodes. The present study starts off with the assumption that the change of matrix that may result from removing a given node would assess the importance of the node since each node make a contribution to the given similarity matrix between nodes. The various matrix norms using the singular values such as nuclear norm which is the sum of all singular values, are used for calculating the contribution of a given node to a node similarity matrix. In other words, we can obtain the change of matrix norms for a given node after we calculate the singular values for the case of the nonexistence and the case of existence of the node. Then, the node resulting in the largest change (i.e., decrease) of matrix norms can be considered as the most important node. Computation of singular values can be computationally intensive when the similarity matrix size is large. Therefore, the singular value update technique is also developed for the case of the network with large nodes. We compare the performance of our proposed approach with other widely used centrality measures using U.S. patents data in the area of information and security. Experimental results show that our proposed approach is competitive or even performs better compared to existing approaches.