How do two adjacent routers know that they have a two-way OSPF communication ?
The fact that a router sees a Hello packet it only shows an INIT state but it does not ensure a two-way communication. Routers include the list of neighbors in their Hello packets, so a 2-way state is reached when a router sees its own ID in the Hellos received from that particular peer.
The Hello packets also contains the information about DR and BDR - or use 0.0.0.0 if they have not been selected yet.
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