Small World Network

A small-world network is a network in which most nodes are not directly connected, but where the neighbors of any given node are likely to be neighbors of each other and most nodes can be reached from every other node by a small number of hops or steps. Specifically, a small-world network is defined to be a network where the typical distance L between two randomly chosen nodes (the number of steps required) grows proportionally to the logarithm of the number of nodes N in the network, that is:

$L\propto \log N$

In Bitcoin, the typical distance between any two nodes is just 1.3.

The economic incentives of mining drive node operators to form what is called a "Small World Network" which we refer to as the Bitcoin Core Network.

This happens over time as miners learn and optimise the network topology over time to create more efficient communication between nodes. This memory function leads to the Core Network forming what is known as a "giant node". This giant node becomes more and more densely connected over time, trending towards a Nearly Complete Graph. The giant node forms the center of a Mandala Network that is what all peers on the Bitcoin network connect via.

A video representation of the Bitcoin network forming a highly connected mesh can be seen [file: here]