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IntroductionBig graphs like social network user interactions and customer rating matrices require significant computing resources to maintain. Data owners are now using public cloud resources for storage and computing elasticity. However, existing solutions do not fully address the privacy and ownership protection needs of the key involved parties: data contributors and the data owner who collects data from contributors. MethodsWe propose a Trusted Execution Environment (TEE) based solution: TEE-Graph for graph spectral analysis of outsourced graphs in the cloud. TEEs are new CPU features that can enable much more efficient confidential computing solutions than traditional software-based cryptographic ones. Our approach has several unique contributions compared to existing confidential graph analysis approaches. (1) It utilizes the unique TEE properties to ensure contributors' new privacy needs, e.g., the right of revocation for shared data. (2) It implements efficient access-pattern protection with a differentially private data encoding method. And (3) it implements TEE-based special analysis algorithms: the Lanczos method and the Nystrom method for efficiently handling big graphs and protecting confidentiality from compromised cloud providers. ResultsThe TEE-Graph approach is much more efficient than software crypto approaches and also immune to access-pattern-based attacks. Compared with the best-known software crypto approach for graph spectral analysis, PrivateGraph, we have seen that TEE-Graph has 10³−10⁵times lower computation, storage, and communication costs. Furthermore, the proposed access-pattern protection method incurs only about 10%-25% of the overall computation cost. DiscussionOur experimentation showed that TEE-Graph performs significantly better and has lower costs than typical software approaches. It also addresses the unique ownership and access-pattern issues that other TEE-related graph analytics approaches have not sufficiently studied. The proposed approach can be extended to other graph analytics problems with strong ownership and access-pattern protection.