Tutte polynomial

The Tutte polynomial is a mathematical tool used to analyze graphs—networks of points connected by lines—by capturing various properties such as connectivity, how the network can be broken apart, or spanning structures. It assigns a polynomial expression to any graph, with different parts of the polynomial providing insights into the network’s robustness, the number of spanning trees, and other features. Essentially, it’s a versatile, compact way to encode complex information about a graph’s structure, useful across disciplines like physics, computer science, and biology to study connectivity and resilience.