This paper shows how algorithmic techniques and parallel processing can speed up general connectivity computation. A new algorithm, called Concurrent Group Search Algorithm (CGSA), is proposed that divides (N-1)N/2 vertex pairs into N-1 groups. Within each group general connectivities of all pairs can be calculated concurrently. Our experimental results show that this technique can achieve speedup of 12 times for one circuit. In addition, group computations are parallelized on a 16-node IBM SP2 with a speedup of 14 times over its serial counterpart observed. Combining the two approaches could result in a total speedup of up to 170 times, reducing CPU time from over 200 hours to 1.2 hour for one circuit. Our new model is better than those without clustering because it characterizes the connection graph more accurately, is faster to compute and produces better results. The best performance improvements are 43% for one circuit and 49% for another.