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Network robustness is an essential system property to sustain functionality in the face of failures or targeted attacks. Currently, only the connectivity of the nodes resilient to an attack is used to assess robustness. We propose to incorporate the properties of the emerging connectivity of the nodes that are affected by the attack (idle network), which is demonstrated to contain relevant information about network robustness, improving the accuracy of its assessment. Our work shows that the information contained in the idle network offers a potential to generalize models, enabling them to estimate robustness for unseen attacks.