An approximate solution for the average number of directed connected subgraphs in an ensemble of random networks with arbitrary degree sequence is presented. Scaling formulas for the number of subgraphs in scale-free random networks are given. It is shown that the subgraph numbers can be very different from those in Erdos random networks. The scaling exponent α exhibits three different scaling laws in three regimes, depending on the control parameter γ.
|Physical Review E
|Published - Aug 2003