The growing popularity of social networks and the massive influx of users have made it challenging to store and process the network/graph data quickly before the properties of the graph change due to graph evolution. Storing graphs or networks that represent entities and their relationships (such as individuals and their friends/followers in a social network) becomes more difficult as the number of users increases, resulting in massive graphs that are challenging to store in standard structures like matrices or adjacency lists. Research in this field has focused on reducing the memory footprint of these large graphs and minimizing the extra memory required for processing. However, there is a trade-off between time and space, as rigorous redundancy removal to achieve a small memory footprint consumes time, and querying becomes more time-consuming when traversing compressed structures compared to matrices or adjacency lists. In this paper, we introduce a parallel technique for constructing graphs using compressed sparse rows (CSR), which offers a smaller memory footprint and allows for parallel querying algorithms, such as fetching neighbors or checking edge existence. We extend our work to include parallel time-evolving differential compression of CSR using the prefix sum approach. Additionally, we measure the speed-up gained by using multiprocessors to compress the graph data. To evaluate our techniques, we perform empirical analysis on massive anonymized graphs, including Live-Journal, Pokec, Orkut, and WebNotreDame, which are publicly available. Overall, our results demonstrate that our proposed methods achieve a smaller memory footprint and faster querying compared to traditional storage structures, with additional speedup gained (up to 83% for the biggest graph with 3.07M nodes and 117.18M edges) through the use of multiprocessors.