Graph theoretic problems are representative of fundamental computations in traditional and emerging scientific disciplines like scientific computing and computational biology, as well as applications in national security. We present our design and implementation of a graph theory application that supports the kernels from the Scalable Synthetic Compact Applications (SSCA) benchmark suite, developed under the DARPA High Productivity Computing Systems (HPCS) program. This synthetic benchmark consists of four kernels that require irregular access to a large, directed, weighted multi-graph. We have developed a parallel implementation of this benchmark in C using the POSIX thread library for commodity symmetric multiprocessors (SMPs). In this paper, we primarily discuss the data layout choices and algorithmic design issues for each kernel, and also present execution time and benchmark validation results.