This article provides a new approach to searching solutions of water transport optimalization problems. It brings a new tool of the graph theory which is the Weighted Adjacency Matrix. This Weighted Adjacency Matrix is suitable for searching for the Minimum Spanning Tree (MST) of the graph. It describes the Weighted Adjacency Matrix as a new element, and shows how it could be used in cases where weighted edges of the graph are given. This creates a new procedure of searching the MST of the graph and completes previously known algorithms of searching for the MST. In the field of ship transportation it could be succesfully used for solutions of optimizing transportation routes where smallest costs are wanted. Proposed Weighted Adjacency Matrix could be used in similar issues in the field of graph theory, where graphs with weighted edges are given. The procedure is shown on the attached example. The paper discusses the application of such route optimization technique forthe maritime sector.