DNA has been considered a promising medium for storing digital information. As an essential step in the DNA-based data storage workflow, coding algorithms are responsible to implement functions including bit-to-base transcoding, error correction, etc. In previous studies, these functions are normally realized by introducing multiple algorithms. Here, we report a graph-based architecture, named SPIDER-WEB, providing an all-in-one coding solution by generating customized algorithms automatically. SPIDERWEB is able to correct a maximum of 4% edit errors in the DNA sequences including substitution and insertion/deletion (indel), with only 5.5% redundant symbols. Since no DNA sequence pretreatment is required for the correcting and decoding processes, SPIDER-WEB offers the function of real-time information retrieval, which is 305.08 times faster than the speed of single-molecule sequencing techniques. Our retrieval process can improve 2 orders of magnitude faster compared to the conventional one under megabyte-level data and can be scalable to fit exabyte-level data. Therefore, SPIDER-WEB holds the potential to improve the practicability in large-scale data storage applications.