On the Generation of Short Paths and Minimal Cutsets of the Hierarchical Web Graph

In the theory of graphs, there exist several algorithms that will find the shortest path between two vertices. Two of these algorithms are due to Dijkstra and Ford. However, an even more general problem would be to develop an algorithm that finds all shortest paths between two vertices in a graph. Furthermore, we may also want to look at minimal ways to cut the edges in a graph such that all shortest paths between two vertices no longer exist. Before we look into this problem, a few definitions are necessary. Definition (1): An s−t path in a graph G is a sequence of vertices (starting at s and ending at t) and edges such that no edge is repeated. Definition (2): A short s − t path in a graph G is a path between two vertices s and t of length ≤ L.