Hadamard Product Decomposition and Mutually Exclusive Matrices on Network Structure and Utilization

Abstract: Graphs are very important mathematical structures used in many applications, one of which is transportation science. When dealing with transportation networks, one deals not only with the network structure, but also with information related to the utilization of the elements of the network, which can be shown using flow and origin-destination matrices. This paper extends an algebraic model used to relate all these components by deriving additional relationships and constructing a more structured understanding of the model. Specifically, the paper introduces the concept of mutually exclusive matrices, and shows their effect when decomposing the components of a Hadamard product on matrices