This paper introduces an innovative symmetric encryption algorithm that utilizes a hybrid graph structure combining properties of star and wheel graphs. The proposed method enhances data security by applying a shift cipher over the plaintext and representing the resulting cipher text values as vertex labels within a structured graph. Edge weights are carefully calculated using algebraic transformations that hide the original values. The recipient decodes the message using inverse operations on graph weights and vertex arrangement. This technique increases encryption complexity, making brute-force decryption significantly more difficult. A case study on the message “HELLO” demonstrates the effectiveness and clarity of the method.