[Data Structure] Weighted Graphs
A weighted graph associates a weight with each edge.
A graph edge's weight, or cost, represents some numerical value between vertex items, such as flight cost between airports, connection speed between computers, or travel time between cities.
A weighted graph may be directed or undirected.
In a weighted graph, the path length is the sum of the edge weights in the path.
The cycle length is the sum of the edge weights in a cycle.
A negative edge weight cycle has a cycle length less than 0.
A shortest path doesn't exist in a graph with a negative edge weight cycle, because each loop around the negative edge weight cycle further decreases the cycle length, so no minimum exists. (minimum = -∞)
