since every peer has to receive every transactions eventually, it seems that Transactions * Peers is the absolute
minimum of transaction sends you'd need. Am I missing something trivial here?
You are!
Imagine if the network were wired such that if a message was relayed along connection 0 on each peer it would form a Hamiltonian cycle and reach every node in the network. Thus, each peer would receive and send each transaction exactly once. This shows the bound cannot be transactions*peers.
OK I see I was just talking about a different quantity. In your ideal example, each transaction
is sent Peers times from someone to someone (which is what I was talking about), though indeed each node only sends it once.
Anyway, this settled, are you saying that currently (without set reconciliation) each node sends each transaction roughly Peers times? (Where Peers is the size of the whole network - not just the number of
neighbours). That's ... pretty bad indeed.