each otherfor some connections in computer network are typically much faster than others (for examplesome edges might represent slow phone-line connections while others might represent high-speedfiber-optic connectionslikewisewe might want to use graph to represent the roads between citiesand we might be interested in finding the fastest way to travel cross-country in this caseit is again probably not appropriate for all the edges to be equal to each otherfor some intercity distances will likely be much larger than others thusit is natural to consider graphs whose edges are not weighted equally weighted graph is graph that has numeric (for exampleintegerlabel (eassociated with each edge ecalled the weight of edge we show an example of weighted graph in figure figure weighted graph whose vertices represent major airports and whose edge weights represent distances in miles this graph has path from jfk to lax of total weight , (going through ord and dfwthis is the minimum weight path in the graph from jfk to lax in the remaining sections of this we study weighted graphs shortest paths let be weighted graph the length (or weightof path is the sum of the weights of the edges of that isif (( , ),( , )(vk - ,vk))then the length of pdenoted ( )is defined as