One thing you might want to know about such a network is the extent to which nodes are connected to other nodes. You could work out the average number of connections per node, but that’s a bit crude. You could also produce a histogram: for each number $x,$ count the number $y$ of nodes that have $x$ connections. When people first started doing this, they noted a curious feature. The variable $y$ often follows a power law; that is, it is proportional to $frac{1}{x^ k},$ where the exponent $k$ is typically small, somewhere between $2$ and $4.$ When this happens the network is called scale free.