FBS Schedule "Chains"

Going by the schedules at FBSSchedules.com, and assuming all FBS teams have their schedules listed, all FBS teams will be "linked" - i.e. it will be possible to construct a chain of one or more games already played between any two FBS teams - after Week 4.

Week 3 cannot be linked because each of Houston, Oregon State, and Texas Tech play the other two and an FCS team in the first three weeks.

The longest chains in Week 4 are 9 games each; there are 11 of them - here is one:
Virginia - North Carolina State (8/29)
North Carolina State - Vanderbilt (9/19)
Vanderbilt - Auburn (9/26)
Auburn - Southern Miss (9/12)
Southern Miss - Tulane (9/26)
Tulane - Kansas State (9/19)
Kansas State - Washington State (9/12)
Washington State - Arizona (9/26)
Arizona - BYU (9/12)