The adjacency matrix calculation based on the acquisition method diagram

It is possible to calculate if there is a path or several paths between two vertices in a graph by the calculation of adjacency matrix, however, the paths themselves cannot be recorded by the calculation of adjacency matrix. This paper proposes an accurate method of calculation by showing the paths of matrices. The operations on path matrices to calculate and record path between two vertices can be very handy and help to determine possible paths more easily. It provides a new method to solve problems efficiently and effectively such as the traveling salesman problem.