A graph G=(V,E,w), where V and E are finite set of vertices and edges respectively, is a directed weighted graph with weights denoted by w(e)>0 for each edge e ∈ E. Given two vertices <s> and <t> ∈ V, P(s,t) is the shortest path between <s> and <t> containing the least sum of edge weights on the path from <s> to <t>. The properties of the graph representation, using matrix structures to represent the graph in normal flow and reverse representations, are considered. Based on these structures, a new algorithm determines the candidate subgraphs and prunes every subgraph that is either unreachable from the given source vertex <s> or does not lead to the given destination <t>, benefiting from the rich information inherent in the matrix and reverse matrix structure representations of the graph. This improves the shortest path algorithm significantly.