Effects of group size distribution on cascading failure in partially interdependent networks

Cascading failures on interdependent networks has attracted much attention in the field of network science. However, the effects of the distribution of group size on cascading failures still puzzled us. In this paper, we propose a cascading failure model on two-layered partially interdependent networks with groups, in which all nodes in the same group are functional dependent on each other. A percolation theory is developed to investigate the final giant component, and the theory well agrees with numerical simulations. Through extensive numerical simulations and theoretical analyses, we find a discontinuous phase transition in the system. In addition, the final giant component increases with the heterogeneity of group size distribution, and the percolation threshold decreases with the heterogeneity of group size distribution. Furthermore, the phase transition is discontinuous for relatively strong dependency, while the phase transition is continuous for relatively weak dependency. The degree distribution of the interdependent networks does not qualitatively alter the above presented phenomena. (C) 2019 Elsevier B.V. All rights reserved.