There is a graph which is an undirected complete graph and the weights of the graph edge are always positive. I select two vertices which are $a$ and $b$ respectively and the two vertices are set at the first time and are fixed points.
How can I set the weight of the edges in order to let the number of shortest paths(between $a$ and $b$ and all shortest paths share the same distance) between $a$ and $b$ (two previously selected vertices) reaches the maximum？
Can I transform this problem into another problem which is related to combination so that I can solve this problems by using the knowledge of discrete mathematics or solve it by using the knowledge of graph theory？
Is there any algorithm that is suitable for my problem？