[takeda]

There is few ISPs that are considered Tier 1 which are considered as the core of the Internet. They have peering agreement between each other to not charge for traffic sent between themselves. This also became something equivalent to "cool club" to join it all existing members need to agree, which is unlikely so currently most common way to become tier 1 is to acquire existing member (like what Verizon did).

So then you have Tier 2 which connect to Tier 1 to have internet access and they pay for it. They are paying for the amount of data being sent. To reduce cost they get into agreements between each other to provide direct connections to other Tier 2 ISPs. So if someone from ISP1 needs to talk to ISP2 they can use that peering link and save cost by not having to send traffic over the core.

There's high incentive to be connected to everyone, no one would be happy to only be able to access just part of the Internet. Remember that unlike what we are used to to home ISPs where we have only a single connections. Businesses and especially ISPs have many links. This is both for redundancy (if something happens to one connection there's a backup) but also to decrease cost and increase performance.