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 minimum distance L between two randomly chosen nodes (the minimum number of steps required) grows proportionally to the logarithm of the number of nodes N in the network, that is:

$L\propto \log N$

The economic incentives of mining drives node operators to form a "Small World Network" which we refer to as the Bitcoin Core Network. The typical distance between any two nodes in the Bitcoin Core Network is just 1.3.

This property is emergent over time as miners learn how to 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 to.

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