Algorithmic Graph Theory

Algorithmic graph theory is the study of designing and analyzing algorithms to solve problems involving graphs — structures made of nodes (vertices) connected by links (edges). It helps us understand how to efficiently navigate, analyze, and optimize networks such as roads, communication systems, or social connections. By developing algorithms, we can find shortest paths, identify clusters, detect cycles, or optimize flows within these networks. This field combines mathematical insights with computer science techniques to solve practical problems involving complex interconnected data, making sense of how different parts of a system relate and how best to manage or improve them.