Analyzing large dynamic networks is an important problem with applications in a wide range of disciplines. A key operation is updating the network properties as its topology changes. In this paper we present graph sparsification as an efficient abstraction for updating the properties of dynamic networks. We demonstrate the applicability of graph sparsification in updating the connected components in random and scale-free networks on shared memory systems. Our results show that the updating is scalable (10X on 16 processors for larger networks). To the best of our knowledge this is the first parallel implementation of graph sparsification. Based on these initial results, we discuss how the current implementation can be further improved and how graph sparsification can be applied to updating other network properties.