Convergence is the state of a set of routers that have the same topological information about the internetwork in which they operate. For a set of routers to have converged, they must have collected all available topology information from each other via the implemented routing protocol, the information they gathered must not contradict any other router's topology information in the set, and it must reflect the real state of the network. In other words: in a converged network all routers "agree" on what the network topology looks like.

Convergence is an important notion for a set of routers that engage in dynamic routing. All interior gateway protocols rely on convergence to function properly. "To have, or be, converged" is the normal state of an operational autonomous system. The Exterior Gateway Routing Protocol BGP typically never converges because the Internet is too big for changes to be communicated fast enough.