© 2021, The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG.Finding the shortest path of complex networks and transportation problems is an important task. Many algorithms have been developed to solve this problem and one of the most well-known is the Dijkstra algorithm, also called “label algorithm”. The graph consists of directed or undirected arc with positive weights as well and Dijkstra’s algorithm can solve both of them. This classical problem in graph theory can be remodeled in a fuzzy environment. The weights of arcs can be expressed with bipolar neutrosophic numbers based on positive and negative effects and the fuzzy graph can be solved with the Dijkstra algorithm for the shortest path problem. This study shows how the Dijkstra algorithm is used to find the shortest path of arcs expressed in bipolar neutrosophic numbers in a single source network. Finally, a numerical example is given to demonstrate the effectiveness of the method.