EIGRP avoids loops by keeping some basic topological information, but it avoids spending too much CPU and memory by keeping the information brief.  When a router learns multiple routes to the same subnet, it puts the best route in the IP routing table.  EIGRP keeps some topological information for the same reason as OSPF, so that it can very quickly converge and use a new route without causing a loop.  EIGRP keeps a record of each possible next-hop router, and some details related to those routes, but no information about the topology beyond the next-hop routers.  This sparser topology information does not require the sophisticated SPF algorithm, resulting in  quick convergence and less overhead, with no loops.

The EIGRP convergence process uses one of two branches in its logic, based on whether the failed route does or does not have a feasible successor route.  If a feasible successor route exists, the router can immediately use that route.  If not, the router must use a query and response process to find a loop-free alternative route.  Both processes result in convergence that is typically less than 10 seconds, but the query response process takes slightly longer.

EIGRP Successors and Feasible Successors

EIGRP calculates the metric for each route to reach each subnet.  For a particular subnet, the route with the best metric is called the successor, with the router filling the IP routing table with this route.  This route’s metric is called the feasible distance.

The routes with a larger metric than the FD for that route requires EIGRP to determine which can be used immediately if the currently best route fails, without causing a routing loop.  EIGRP runs a simple algorithm to identify which routes can be used, keeping these loop-free backup routes in its topology table and using them if the currently best route fails.  These alternative, immediately usable routes are called feasible successor routes, because they can feasibly be used when the successor route fails.  A router determines if a route is a feasible successor based on the feasibility condition: If a nonsuccessor route’s RD is less than the FD, the route is a feasible successor route.

EIGRP decides if a route can be a feasible successor if the reported distance for that route (the metric as calculated on that neighbor) is less than its own best computed metric (the FD).  When that neighbor has a lower metric for its route to the subnet in question, that route is said to have met the feasibility condition.

Ok so a quick note to myself: The way to understanding this, is it is comparing its own feasibility against another routers feasibility.  So the examples aren’t saying Router E can get to subnet 1 through router C at 13000, versus the 14,000 it is getting there through at router D.  It is saying that Router C can get ITSELF there with a metric of 13,000.  That is how the feasible successor is chosen.