Tier-2 reachability and multihoming

[G Pavan Kumar <pavanji () cse iitb ac in>]

Hi there,
         I have been working on characterizing the internet hierarchy.
I noticed that 27% of the total possible tier-2 provider node pairs are
unreachable i.e., they dont have any tier-1 node connecting them nor a
direct peering link between them.
      Multihoming can be used as a predominant reason for the
reachability of tier-3 nodes which are customers of these nodes, but what 
about the reachability of tier-2 nodes themselves and its customers which 
cannot afford to multihoming? How does BGP solve this reachability problem 
when it gets a request to a prefix unreachable?

       1        tier-1
     /
   2      4     tier-2
  / \    / \
 5   6  7   8  tier-3

here, nodes 2 and 4 have no reachability,
       1
     / |
   2   3  4
  / \   \/ \
 5   6  7   8

now, node 7 is reachable from 2 and its lower level nodes, but what
about
node 4 and 8, and as a typical case, suppose nodes 4 and 8 have no
multihoming whatsoever, what then?

Regards,
pavan