In any route or in any networks of roads, there is at least one shortest path to reach from one point to another. Such shortest path in form of graph is said to be the shortest path Problem. In other words, it is the way to minimize the weights of the constituent edges in finding a path between two vertices (or nodes) in a graph. Additionally, if one needs to visualize what Shortest path problem then one can consider the travel path of FED-EX to deliver the packages using shortest time and distance. This approach is normally used in web mapping sites such as MapQuest or Google Maps.
(6, 4, 5, 1) and (6, 4, 3, 2, 1) are both paths between vertices 6 and 1. Source: Wikipedia
Similarly, there are lots of Algorithms associated with Shortest Path Problem but the Dijkstra’s algorithmic by Leyzorek et al. 1957; Dijkstra 1959 is considered to be the best. Dijkstra's algorithm solves the single-source shortest path problems.