Memory access is known to be the main bottleneck for shared-memory parallel graph applications especially for large and irregular graphs. Propagation blocking (PB) idea was proposed recently to improve the parallel performance of PageRank and sparse matrix and vector multiplication operations. The idea is based on separating parallel computation into two phases, binning and accumulation, such that random memory accesses are replaced with contiguous accesses. In this paper, we propose an algorithm that allows execution of these two phases concurrently. We propose several improvements to increase parallel throughput, reduce memory overhead, and improve work efficiency. Our experimental results show that our proposed algorithms improve shared-memory parallel throughput by a factor of up to 2× compared to the original PB algorithms. We also show that the memory overhead can be reduced significantly (from 170 percent down to less than 5 percent) without significant degradation of performance. Finally, we demonstrate that our concurrent execution model allows asynchronous parallel execution, leading to significant work efficiency in addition to throughput improvements.