The shortest path problem (SPP) in graph theory is the problem of assessing a path between two vertices in a graph to minimize the sum of the weights of the edges of its constituent. The SPP ia classical and elementry problem of a graph theory which is applicable in many fields like GIS network analysis, computational geometry, operational research and graph algorithms. SPP are among the elementry problems studied in network optimization. Graphs are very important models of networks. Path-solutions, including location-based services and web-based GIS services, are becoming an important component of many GIS applications. In this paper, we introduced a new method to solve SPP in a network. The SPP is fundamental problems in network optimization. Most traditional solutions for path-finding depends on the shortest path algorithms which tend to minimize travel cost between points. These algorithms use cost criteria which are generally the edge attribute of the graph network. There is a neutrosophical shortest path study in this paper with a vague neutrosophic number (VNsN) on a network. A suggested algorithm also provides the shortest path length (SPL) from source vertex to destination vertex with the ranking function. Here, a VNsN is allocated to each arc length. Lastly, there is a numerical example showing the method proposed.
