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Data security is an important component of data communication and transmission systems. Its main role is to keep sensitive information safe and integrated from the sender to the receiver. The proposed system aims to secure text messages through two security principles encryption and steganography. The system produced a novel method for encryption using graph theory properties; it formed a graph from a password to generate an encryption key as a weight matrix of that graph and invested the Least Significant Bit (LSB) method for hiding the encrypted message in a colored image within a green component. Practical experiments of (perceptibility, capacity, and robustness) were calculated using similarity measures like PSNR, MSE, and SSIM. These measures had proved the efficiency of the system for image quality and hiding messages with PSNR ratio more than 85 dB, MSE ranged (4.537e-05 to 5.27546e-04) and SSIM=1.0 for using a cover file with size ranged from 256×300 to 1200×760 pixels and message ranged from 16 to 300 characters.