  In this paper, we present an on-line fully dynamic algorithm for maintaining
strongly connected component of a directed graph in a shared memory
architecture. The edges and vertices are added or deleted concurrently by fixed
number of threads. To the best of our knowledge, this is the first work to
propose using linearizable concurrent directed graph and is build using both
ordered and unordered list-based set. We provide an empirical comparison
against sequential and coarse-grained. The results show our algorithm's
throughput is increased between 3 to 6x depending on different workload
distributions and applications. We believe that there are huge applications in
the on-line graph. Finally, we show how the algorithm can be extended to
community detection in on-line graph.
