Encryption plays a significant role in data security against unauthorized access. However, its criticality is threatened by the advancements in computing infrastructure and cryptanalysis attacks with the advent of quantum computing, inducing the need for new and improved techniques. This paper introduces the NR2 Graph-Based Encryption Algorithm. The key innovation lies in leveraging the property of hypergraphs, which link multiple vertices with a single hyper-edge, unlike traditional graphs that connect only two vertices. This hypergraph and a randomly generated key, aided by a random sequence, generate cipher text through a sequence-driven process which incorporates randomness and effectively obscures the relationship between the elements. This introduces computational complexity and minimizes predictability. The algorithm’s competitiveness with existing techniques is demonstrated using key metrics like security, efficiency, and resistance to attacks. The findings demonstrate the NR2 algorithm’s superior resilience against brute force attacks with a cost of \(31^{31}\) permutations, and an encryption efficiency comparable to industry benchmarks. It explores the prospect of utilizing complex structures like a hypergraph to strengthen encryption against brute force and cryptanalysis attacks when compared to already established standards like AES and RSA, to deliver a higher level of security.