I think I have a miss understanding of what the network statement is for in EIGRP.
Does the network statement say what networks to talk about or what networks to talk to?
Yes, assuming that your EIGRP uses AS 1, you would put that command on each interface of the core. The core would see all of the detail routes. But the other routers would have only a single entry in their routing table for the p2p links.
We are making good progress in getting this cleared up. Jon has explained well that (assuming no distribute lists or other route advertisement filtering) that an EIGRP router will advertise to neighbors routes that it has dynamically learned as well as advertising local routes controlled by the network statement.
Just to clear up one other thing from your post. You say that:
Router B has interfaces only in 10.0.0.0 However Both are network statements in EIGRP
If Router B has interfaces only in network 10.0.0.0 then there is no need to have a network statement for 192.168.0.0. It does not hurt anything if it is there, but it does no good to have it. It is superflous.
"Would it make the explanation even more complicated to talk about advertising routes in the table that are not locally connected"
I think this is what Rick meant by the above. Router B will receive a route for 192.168.0.0 from Router A. Router B will then advertise this route for 192.168.0.0 to Router C. This is normal routing behaviour, well at least for EIGRP/RIP/IGRP. OSPF is slightly different.
The network statement only controls the neighborships formed and the local networks advertised. Any routes received via EIGRP from another router will still be advertised on.