An autonomous system has 7 routers configured with BGP.

Full Mesh Requirement: In a BGP network, to ensure that all BGP routers within the same autonomous system (AS) have complete reachability, each router must establish an iBGP session with every other router in the AS.

Calculating the Number of iBGP Sessions:

The formula to calculate the number of iBGP sessions required in a fully meshed configuration is ????(????−1)22n(n−1)​, where ????n is the number of routers.

For an autonomous system with 7 routers, we substitute ????=7n=7 into the formula.

Applying the Formula:

7(7−1)2=7×62=422=2127(7−1)​=27×6​=242​=21

Explanation:

Each of the 7 routers needs to establish a session with every other router, but each session is counted only once. Therefore, we divide the product of the total routers and one less than the total routers by 2 to avoid double-counting.

This results in a total of 21 iBGP sessions.

References:

Nokia Border Gateway Protocol Fundamentals

Standard BGP configuration guidelines and best practices