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

TL;DR

This paper introduces mutually exclusive matrices and explores their role in Hadamard product decomposition, enhancing the algebraic modeling of transportation networks and their utilization patterns.

Contribution

It presents a novel algebraic framework incorporating mutually exclusive matrices to better understand network structure and utilization in transportation science.

Findings

Mutually exclusive matrices influence Hadamard product decomposition.

The extended algebraic model provides deeper insights into network components.

Application to transportation networks improves understanding of flow 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