Social networks provide a basis for collective resilience to disasters. Combining the quasi-experimental context of a major earthquake in Ya’an, China with anonymized mobile telecommunications records regarding 91,839 Ya’an residents, we use initial bursts of post-disaster communications (e.g., choice of alter, order of calls, latency) to reveal the ‘important ties’ that form the social network backbone. We find that only 26.8% of important ties activated during the earthquake were the strongest ties during normal times. Many important ties were hitherto latent and weak, only to become persistent and strong after the earthquake. We show that which ties activated during a sudden disaster are best predicted by the interaction of embeddedness and tie strength. Moreover, a backbone of important ties alone (without the inclusion of weak ties ordinarily seen as important to bridge communities) is sufficient to generate a hierarchical structure of social networks that connect a disaster zone’s disparate communities.