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

¹ College of Mathematics and Physics, Shanghai University of Electric Power - Shanghai 200090, China
² Engineering Research Center of Software/Hardware Co-design Technology and Application, Ministry of Education (East China Normal University) - Shanghai 200062, China
³ School of Information Science and Technology, Fudan University - Shanghai 200433, China
⁴ Shanghai Artificial Intelligence Laboratory - Shanghai 200232, China

^(a) E-mail: qianjianghai@shiep.edu.cn (corresponding author)
^(b) E-mail: ddhan@fudan.edu.cn (corresponding author)

Received: 7 December 2022
Accepted: 20 April 2023

Abstract

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 k_c. 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.