A special matrix power operation development for simultaneous calculation of all network's shortest path

Network's shortest paths calculation is an important need in transportation network analysis. The Dijkstra algorithm has long been developed for the shortest path of a pair of nodes calculation individually. A more practical method to simultaneously calculate all shortest paths of all pair of nodes of a network needs to be developed. This paper presents the development of a method to calculate simultaneously all shortest paths of all pairs of nodes of a network. This calculation method, called a Min-Plus Algebra, is a modification of Max-Plus Algebra, having a special Matrix Power Operation, enable and easier to be executed in spreadsheet software.