Yes, In EIGRP world Router ID does exist. However the significance of the EIGRP Router ID is not as important as Router ID in OSPF or BGP. But there are some situations where you might need to take a look at it in order to troubleshoot EIGRP connectivity/reach-ability issues.
Yeah I know, it sounds kind of weird but it's really not that ugly.
So the first thing that comes in mind is How can I see EIGRP Router ID ?
Simple, just use the following command "sh ip eigrp topology" and you can find it right there :)
Now next thing comes in mind is what's it's significance and how it can create problem ?
Now before that I would like to tell you guys the Router ID selection criteria in EIGRP is same as in OSPF.
Now lets talk about it's significance for a moment. EIGRP Router ID don't have any local significance as far I know based on my different testing scenarios. Even if it's DUPLICATE within AS, it's not gonna hurt. But on the other hand in OSPF - duplicate router id can create lots of Database inconsistency issues because as per Link State protocol theory - All routers within the OSPF area must have same set of Link State Database copies and LSA's are tracked by sending Router's router id.
Now if talk about problems, based on my different testing scenarios I found that EIGRP router id can create problems when we are redistributing external prefixes like redistributing Static routes, Other EIGRP AS, OSPF , Connected Subnets etc....
Below I am attaching all my testing results one by one. Hopefully everything is simple and straight to understand but incase you need some more explanation then just drop me an email at - email@example.com
Don't forget to click on images to view better :)
Also read outputs starting from left side and later from right side *Up side Down too*
Image 1 - Order->R1, R2
Image 2 - Order->R3, R4
Image 3 - Order->R1, R2, R4, R3
Image 4 - Order->R4, R3, R4
Image 5 - Order->R3, R1, R1, R3, R2
Image 6 - Order->R3