Due to the dramatic increase in the availability of dynamic data in various domains, including computational social systems, there is a need to formulate processing and analysis methodologies that can efficiently incorporate data changes while reducing recomputations. This is especially critical for network analysis techniques where current methodologies pursue strategies based on maintaining intermediate or partial results. However, there are critical trade-offs with respect to memory and processing time overheads that have prevented these designs from scaling with larger network sizes and higher rates of network dynamism. In this work, we demonstrate the capability of our anytime anywhere framework to formulate closeness centrality algorithms that can adapt to memory availability by varying the number of partial results that are stored and maintained over the course of the analysis. Additionally, using a combination of theoretical analysis and experimental results we compare the performance of these algorithm designs, and identify conditions under which one design performs better than the others.