Scale-free network model under exogenous pressures

A random network model under the constraint that the average distance and the average degree (k) remain approximately constant is studied. We found that, if the network maintains the form of its degree distribution and the maximal degree k(c) is a N-dependent cutoff function k(c)(N) < N, the degree distribution would be approximately power-law whose exponent is between 2 and 3. Moreover, the distribution exponent has little relationship with the average degree (k). The average distance constraint can be interpreted as the environmental selection pressure, which could explain the scale-free degree property of real-world networks.