Abstract
In this study, we present a novel analytical approach for robustness on Erdos-Renyi (ER) networks by introducing statistical physics method. We establish an exact mapping relation between ER networks and Ising model. Based on the mapping relation, we obtain the partition function of the ER networks and use it to determine the size of the giant component and the value of the critical edge present probability in ER networks. We extend the approach to investigate the size of remaining giant component and the critical fraction of the nodes removed in the ER networks whose nodes under the randomly attack.
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