With the wide deployment of public clouds, proprietors of big graphs need to utilize the cloud to deal with the scalability issues. However, the privacy and ownership for graphs in the cloud has turned into a major concern. In this project, we examine privacy-preserving algorithms for graph spectral analysis of outsourced encrypted graph in the cloud. We consider a cloud-centric structure with three collaborative: information donors, information proprietor, and a genuine yet inquisitive cloud supplier. For a N×N diagram framework, our calculations accomplish a handy work portion with saved security: the cloud handles costly capacity and calculation in O(N2) many-sided quality, and information proprietor and information patrons’ calculations taken a toll just O(N). We have built up the protection safeguarding adaptations of the two estimated eigendecomposition calculations: the Lanczos calculation and the Nyström calculation, in view of various encryption techniques: added substance homomorphic encryption (AHE) strategies and to some degree homomorphic encryption (SHE) strategies. Both thick and meager networks are considered, while inadequate lattices likewise include a differentially private information accommodation convention to permit the exchange off between information sparsity and security. Test comes about demonstrate that the Nyströ calculation with meager encoding can significantly diminish information proprietors’ costs; SHE-based techniques have bring down computational time while AHE-based strategies have bring down correspondence costs.