Many large datasets from a variety of fields of research can be represented as graphs. A common query is to identify the most important, or highly ranked, vertices in a graph. Centrality metrics are used to obtain numerical scores for each vertex in the graph. The scores can then be translated to rankings identifying relative importance of vertices. In this work we focus on Katz Centrality, a linear algebra based metric. In many real applications, since data is constantly being produced and changed, it is necessary to have a dynamic algorithm to update centrality scores with minimal computation when the graph changes. We present an algorithm for updating Katz Centrality scores in a dynamic graph that incrementally updates the centrality scores as the underlying graph changes. Our proposed method exploits properties of iterative solvers to obtain updated Katz scores in dynamic graphs. Our dynamic algorithm improves performance and achieves speedups of over two orders of magnitude compared to a standard static algorithm while maintaining high quality of results.