Hello Wassim,

>> What if I put 3 or 4 instead of 2? will it affect the BGP neighbor establishment?

the eBGP session will be established but what changes is that the eBGP session could be able to stay up even if the direct link between the two routers is down if the topology provide an alternate path via another node.

So for example a BGP conditional advertisement is not triggered or you can face security problems.

Once I used for some years 3 for eBGP session between loopbacks. Then in developing an MPLS VPN service in a VRF site using one CE and two PE I saw the session PE1-CE still up after having disabled the link PE1-CE and by reducing from 3 to 2 I've corrected the behaviour.

The two PE routers had a direct MPLS link (backbone LAN) so that 3 was enough to have the eBGP session still up but BGP packets and user traffic were using the link PE2-CE

Hope to help

Giuseppe