Consider a network of two PCs, PC1 and PC2, connected to each other through a router. Note that the network is symmetrically disposed to PC1 and PC2. Once booted, the PC's run ospfd (over Quagga) and the router run OSPF. After giving sufficient time (maybe an hour) for the OSPF to converge, can I expect PC1 and PC2 to have symmetrical routing tables (i.e. one contains PC2 in place of the other's PC1 entry)?
More generally, suppose I have a large network of many hosts, divided into several subnets, interconnected through routers, all running OSPF. If there are 2 hosts or routers placed symmetrically in the network, will they have symmetrical routing tables once OSPF converges?