| Shortest Paths
				Our next step in generalizing the notion of a graph is to consider
				weighted graphs, for which every edge is
				associated with a real number, called a weight
				(or cost, or length) of the
				edge. Weights can be negative or nonnegative.
				 
				This generalization prompts us to modify our definition of the length
				of a walk, which we are going to call the weight of a	walk
				in order to differentiate it from the notion of the
				number of edges in a walk.
				 
				Here is the formal definition of the weight of a walk:
				 
				Given a weighted directed graph
				 with a weight function  ,
				the weight  of a walk 
				 Equation
				1 
				is defined as the sum
				 
				 Equation
				2 
				The distance
				 from  to  is defined by 
				
				 Equation
				3 
				if no directed walk from
				 to  exists    is a directed walk from  to   |