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EIGRP build topology table to store all learned routes (i.e. beast and non beast routes), the beast route in the EIGRP terminology is successor route, but the routing algorithm (DUAL) that used by EIGRP protocol select one or more backup rout for the beast one if applicable (i.e. in another words if it met feasibility conditions) called feasible successor, once successor route failed, the feasible one will be successor immediately, otherwise EIGRP will do change process steps.
Successor (best route) and Feasible Successor (Second Best Route) are listed in the topology table. Since EIGRP is known for fast convergence and the concept of successor and feasible successor makes it possible.
Hope you find this helpful.
Thanks.
Successor is the best route from source to destination where the metric(feasiable distance) is lowest than all other neighobour metric(reported distance.) and feasible successor is the next best route or backup route.
Successor route is in routing table(show ip route) and feasible successor route is in topology table(show ip eigrp topology)...
Thanks
Jaher Ullah
The successor is exactly how Jaher describe,
The feasible Successor : is the next best metric with the feasible condition ( AD<FS) satisfied :
Feasible condition means that any route wants to be a feasible successor; the advirtised distance of that route must be lower than the metric of the best route.