I'm witing because i've been working on a project, in this project The user has to give the initial city an the final. I've read about the Floyd's Algorithm. In my project i just have to use the final step of Floyd's Algorithm that is to check the final adjacency matrix, given by me.

i just have to use the final step of Floyd's Algorithm that is to check the final adjacency matrix, given by me First things first. An adjacency matrix for your image of five nodes would have five rows and five columns. The value for each cell is taken from the image/graph values. There may be several ways to go about this such as using a large number/infinity in the adjacency matrix for one-way direction/no connection or using a separate matrix with binary or boolean values. If we use the large number approach, then moving from node 3 to node 5 gives a matrix cell value of 15; moving from node 5 to node 3 calls for a cell value of a large number (infinity, not possible in the workings of Floyd's algorithm which tests for minimums). With this approach, to check for a direct route between two nodes we look for a cell value that is not zero (start node == end node) or infinity/large. If you want to find the route of lowest/minimum value we need to consider every possible path between the two nodes. This includes the direct node-to-node path just mentioned and then all paths with one intermediary step between start and end. Then all possible paths of two intermediary steps between start and end nodes. And for paths of increasing intermediary steps up to the limit of numberOfNodes minus the start and stop node selections; for your image: 5 - 2 = 3. Then for each possible path, add up the values along the path segments obtained from the adjacency matrix and save the lowest total along with the corresponding path.