This article offers a novel perspective on identifying the critical branches under load redistribution (LR) attacks. Compared to the existing literature that is largely disruption-driven and based on dc state estimation, we propose to address the threat from LR attacks on a more fundamental level by modeling and analyzing the circulation of false data within the cyber network resulting from the coordinated branch and node measurement manipulation based on ac state estimation. We reveal the underlying mechanism that disturbing the coordinated and reconciled interactions among false data injections can effectively sever the completeness and consistency of the LR attack, thus reducing its damaging effect. We then develop a scalable and computationally efficient critical branch identification approach that evaluates and ranks branches in terms of their criticality according to the graph model of the false data circulation. Case studies are conducted on IEEE 14-, 39-, 118-bus systems and several large-scale models to validate the effectiveness and computational efficiency of the proposed approach. Simulation results show that the proposed approach scales well with the size of the system and can effectively mitigate the damaging effects of the LR attack in terms of operation cost and load shedding.