Graph theory is the study of networks: objects (vertices) connected by relationships (edges). Born from Euler's 1736 solution to the Königsberg bridge problem, it now underpins everything from GPS navigation and social networks to chip design and epidemiology. Many of its core questions — shortest paths, optimal colorings, maximum flows — are deceptively simple to state yet profoundly difficult to solve in general.
These simulations let you build, manipulate, and analyze graphs in real time. Watch Dijkstra's algorithm fan outward to find the shortest path. See a minimum spanning tree grow edge by edge. Experiment with chromatic numbers, push flow through a network, and trace Eulerian circuits across every edge exactly once.