Abstract: To study the robustness of complex networks under attack and repair, we introduced a repair model of com- plex networks. Based on the model, we introduced two new quantities, i. e. attack fraction f and the maximum degree of the nodes that have never been attacked Ka , to study analytically the critical attack fraction and the relative size of the giant component of complex networks under attack and repair, using the method of generating function. We showed ana- lytically and numerically that the repair strategy significantly enhances the robustness of the scalcfrec network and the effect of robustness improvement is better for the scale-free networks with smaller degree exponent. We discussed the application of our theory to the understanding of robustness of complex networks with reparability.

Key words: Reliability, Repairing model, Warship fleet complex networks