Social networks — Finding communities in social networks.
Physics — The Ising model of magnetism, where atoms have spin up or spin down and interact with neighbors, maps onto MaxCut.
Circuit design — When laying out a circuit board, you want to minimize wires crossing between two regions - this is the closely-related MinCut problem!
Image processing — Separating an image into foreground and background.
Computer science — Computer scientists study MaxCut because it is "NP-hard", meaning that it is just as hard to solve as a bunch of other important problems. If you find a good algorithm for MaxCut, it can be used for all these other problems!
Move each node to the left (0) or right (1)
Your score is the number of edges that are cut by the dashed line between left (0) and right (1)
Try to MAXimize the number of edges CUT — find the MaxCut!