A network in mathematics is merely a group of connected objects that is formalized through the use of graphs. The shortest path or route problems can be applied to search for a classic sequence of options with a fixed target state. In this paper, a new philosophy on the shortest path is defined by a pragmatic approach. It deals with the possible variable scaling of the merits without changing the ranks. The ranks are constant, but the scales are varied. A great number of shortest-path algorithms are studied in the literature. This work defines a new HB Optimum Method, an innovative and more suitable method. There are four types of HB Optimum methods- One-sided Increment, One-sided Decrement, Two-sided Change in two elements, and Two-sided change to n elements. The HB shortest path method is defined by taking the existing shortest path algorithms as a base or input, and weights of distinct edges of the first and the second path are revised without changing the ranks of the paths. The generic mathematical model and an algorithm of the same are presented in this work. This paper explains two new concepts, the Maxmin path and the Minmax path of any weighted connected graph. Moreover, HBSPM is more advanced than Dijkstra's and Prim’s Algorithms. The HBSPM works well for Dense and Sparse graphs also. This work has numerous applications in science, technology, and real-life circumstances. The HBSPM helps to decide the increments/decrements in the price of an article, profit margins, wireless networks, possible variation in grades, and many more.

Shortest path algorithm, HB Optimum Method, Dijkstra’s Algorithm, Prim’s Algorithms