Double power-law distribution in spatial network induced by cost constraints

We investigate the scaling laws of the degree distribution in an evolving spatial network where the long-range links of a node are subject to a cost constraint. The constraint can cause a discontinuous reduction in the length of the links to be attached to the node once the node reaches some critical degree kc. We show that this effect can result in an abrupt change in the attachment probability and consequently induces a double power-law degree distribution. We derive the distribution analytically for the homogeneous constraint and demonstrate a consistent result for the heterogeneous one. Our model finds a robust connection between the double power law and the spatial constraint and offers a plausible explanation of the common occurrence of the distribution in airline networks.