This research focuses on accelerating the computational time of two base network algorithms (k-simple shortest paths and minimum spanning tree for a subset of nodes)-cornerstones behind a variety of network connectivity mining tasks-with the goal of rapidly finding network pathways and trees using a set of user-specific query nodes. To facilitate this process we utilize: (1) multi-threaded algorithm variations, (2) network re-use for subsequent queries and (3) a novel algorithm, Key Neighboring Vertices (KNV), to reduce the network search space. The proposed KNV algorithm serves a dual purpose: (a) to reduce the computation time for algorithmic analysis and (b) to identify key vertices in the network (context). Empirical results indicate this combination of techniques significantly improves the baseline performance of both algorithms. We have also developed a web platform utilizing the proposed network algorithms to enable researchers and practitioners to both visualize and interact with their datasets (PathFinder: http://www.path-finder.io).