With its origin in sociology, Social Network Analysis (SNA), quickly emerged and spread to other areas of research, including anthropology, biology, information science, organizational studies, political science, and computer science. Being it's objective the investigation of social structures through the use of networks and graph theory, Social Network Analysis is, nowadays, an important research area in several domains. Social Network Analysis cope with different problems namely network metrics, models, visualization and information spreading, each one with several approaches, methods and algorithms. One of the critical areas of Social Network Analysis involves the calculation of different centrality measures (i.e.: the most important vertices within a graph). Today, the challenge is how to do this fast and efficiently, as many increasingly larger datasets are available. Recently, the need to apply such centrality algorithms to non static networks (i.e.: networks that evolve over time) is also a new challenge. Incremental and dynamic versions of centrality measures are starting to emerge (betweenness, closeness, etc). Our contribution is the proposal of two incremental versions of the Laplacian Centrality measure, that can be applied not only to large graphs but also to, weighted or unweighted, dynamically changing networks. The experimental evaluation was performed with several tests in different types of evolving networks, incremental or fully dynamic. Results have shown that our incremental versions of the algorithm can calculate node centralities in large networks, faster and efficiently than the corresponding batch version in both incremental and full dynamic network setups.