Continuous Phase Transition of k-Partite Networks

Abstract

Our daily lives rely on all kinds of complex networks. However, complex networks in reality often suffer from random failures and/or attacks that can cause failures to their nodes/edges. A network can totally lose its functionalities due to nodes/edges failures. It is, therefore, of great significance to assess the robustness of complex networks confronted with failures. The network robustness analysis is helpful for assuring the reliability of complex networks. In our previous work, we had experimentally investigated the robustness of a special type of networks called k-partite networks. Simulation results have discovered that k-partite networks are robust to random node failures. In this work, we aim to investigate the underlying mathematical principle for the robustness property of k-partite networks. To do so, we have developed the mathematical theory to calculate the robustness of k-partite networks to random node failures. The developed theory mathematically uncovers the continuous phase transition of the robustness of k-partite networks under random node failures. In order to check if the developed theory is correct, we experimentally test the robustness of computer generated k-partite networks. The experimental results and the one calculated using the proposed theory comply with each other, which proves that the proposed theory is correct.