A Brief Overview of Applications of Tree-Width and Other Graph Width Parameters

Graph theory, a fundamental branch of mathematics, centers on the study of networks composed of vertices (nodes) and edges, examining their paths, structures, and properties. One essential metric in this field is the ”graph width parameter,” which quantifies the maximum width across all cuts or layers within a hierarchical decomposition of the graph. Tree-width, in particular, has garnered significant attention due to its broad range of applications. In this work, we revisit these parameters and their applications, focusing specifically on tree-width and related graph width parameters in the contexts of Bond Graphs, Factor Graphs, and Graph Entropy.