How we find the smallest path by using weighted Graphs?

How we find the smallest path by using weighted Graphs?

In the weighted graph each node a packet switch in the network (individual computers are not part of the graph) are given the weight of label that may be consisting of any cost like time, expense, bandwidth and any other the route is calculated for each destination or next node based on the sum of these weights on different paths and the shortest path based on less sum of weight is selected for that node.