For example system A can use telnet to contact system B, but system B cannot use telnet to contact system A. Further questioning of the user revealed that this problem appeared shortly after a power failure.
For troubleshooting use the traceroute utility to show the route that network traffic takes from system B to system A. If the traceroute output reveals route that goes via additional system (let's call it system C) you have a rogue router problem.
Often that happens due to the fact that system C had been modified by an end-user. For example an additional interface was added, bit the user did not add /etc/notrouter file to the system. In this case, after rebooting the system, it came up as a router and started advertising routes, which confuses the core routers and disrupts network traffic patterns.