Treewidth

Treewidth is a measure of how closely a network or graph resembles a tree. A tree is a simple structure with no cycles, making problems on it easier to solve. Treewidth quantifies the complexity of a graph by indicating how "tree-like" it is—smaller treewidth means more tree-like and generally easier to analyze computationally. Think of it as a score: the lower the score, the more manageable the graph for certain algorithms. Many complex problems become simpler when restricted to graphs with low treewidth, which is useful in fields like database theory, AI, and network analysis.