Adaptive SIS network: Nodes are S (susceptible, blue) or I (infected, red). S-I edges spread infection with rate β. Infected nodes recover at rate γ. Rewiring: with rate φ, a susceptible node breaks its link to an infected neighbor and rewires to a random susceptible node. This coevolution drives a fragmentation transition: above a critical φ, the network splits into disconnected clusters of susceptibles, blocking disease spread. Below φ_c, infection pervades the whole network.