See the network in Figure 1 below. Source node 1 fails, which from a pure availability perspective disrupts only traffic originating or terminating at node 1 because all other nodes can still communicate. So a coherent network (as is the one in the figure) continues to be coherent after this failure, as it must due to the definition of coherent.
But now consider performance. Say the traffic from node 1 (for our example, between nodes 1 and 4, but not necessarily) was significant enough to constrain the traffic traversing the network between nodes 2 and 3. For example, the node in the center of the figure may be insufficient for the demand on the network. Traffic between nodes 2 and 3 cannot be adequately carried when all resources in the network are working. From their perspective, the service fails when the network is fully working. But when node 1 fails, suddenly resources are free, and the network can now carry all the traffic between nodes 2 and 3. When the network fails in this way, the network suddenly works from the perspective of nodes 2 and 3.
This situation demonstrates incoherent behavior in a network when capacity constraints are considered. The example network is simple, but clearly extends to the more complex, realistic case. This case, which we may all reference, resulted from a conversation with a colleague where we concluded that this type of incoherent behavior was often forgotten.
Fig. 1. A simple network to illustrate incoherent behavior under capacity constraints.
NOTE: Special thanks to Troy Houston from SevOne for pointing out an error in an earlier version of this post.