An interesting phenomenon in growing random networks:
The number of 3-node, 3-edge connected subgraphs in a random, scale-free network of
N nodes scales as N
0 (=1). No matter how big your network grows, you're going to have a roughly constant number of 3-node, 3-edge subgraphs that depends only on the ratio of edges to nodes.
Let's back up a minute before we see why this counterintuitive result is so and what it means. Imagine that we have a network made up of
N nodes connected by
E edges. You can start out with two nodes connected by one edge: