The "six degrees of separation" arises because the graph has a particular shape that gives it that property, such as the mostly-power-lawish shape that human re

The "six degrees of separation" arises because the graph has a particular shape that gives it that property, such as the mostly-power-lawish shape that human relationships have. It is not a general characteristic of graphs. While we know this model is too stupid-simple to be the whole story, if you imagine the universe as a naive 3d grid graph with nodes at evenly-space intervals where everything takes place, there is no "six degrees of separation" effect; distances between one node and another would be the Manhattan distance, with no N-node shortcut to another point available on average. (Already we see why this graph can't be our universe; our universe does not use the Manhattan distance metric for distance.)