This paper introduces iRun, a lossless graph compression algorithm that compresses graphs by dividing them into horizontal and vertical regions (HVR) for efficient compression. The algorithm improves compression ratios by considering both horizontal and vertical-shaped regions, which allows for better compression than traditional fixed-size block methods. The proposed technique achieves an average compression ratio of 93.8%, outperforming existing state-of-the-art graph compression methods. The iRun algorithm processes graph data by decomposing the adjacency matrix into subblocks and applying different compression algorithms to each subblock based on their shape and density. It uses parallel processing to select the best compression algorithm for each block, reducing storage requirements and improving processing efficiency. The algorithm also includes a sparsity check to determine whether a block is dense or sparse, and then applies the most suitable compression method. The results show that iRun outperforms existing compression techniques in terms of compression ratio, processing time, and memory usage. The paper also compares iRun with four existing bitmap compression algorithms and four encoding schemes for graph compression. The experimental results demonstrate that iRun provides a more efficient compression ratio and better performance in terms of processing time and memory usage. The algorithm is designed to work with real-world graphs that exhibit a power-law distribution, which is common in social networks and other large-scale graph datasets. The iRun technique is efficient and can be applied to a wide range of graph data, making it a promising solution for graph compression in data mining and graph processing applications.This paper introduces iRun, a lossless graph compression algorithm that compresses graphs by dividing them into horizontal and vertical regions (HVR) for efficient compression. The algorithm improves compression ratios by considering both horizontal and vertical-shaped regions, which allows for better compression than traditional fixed-size block methods. The proposed technique achieves an average compression ratio of 93.8%, outperforming existing state-of-the-art graph compression methods. The iRun algorithm processes graph data by decomposing the adjacency matrix into subblocks and applying different compression algorithms to each subblock based on their shape and density. It uses parallel processing to select the best compression algorithm for each block, reducing storage requirements and improving processing efficiency. The algorithm also includes a sparsity check to determine whether a block is dense or sparse, and then applies the most suitable compression method. The results show that iRun outperforms existing compression techniques in terms of compression ratio, processing time, and memory usage. The paper also compares iRun with four existing bitmap compression algorithms and four encoding schemes for graph compression. The experimental results demonstrate that iRun provides a more efficient compression ratio and better performance in terms of processing time and memory usage. The algorithm is designed to work with real-world graphs that exhibit a power-law distribution, which is common in social networks and other large-scale graph datasets. The iRun technique is efficient and can be applied to a wide range of graph data, making it a promising solution for graph compression in data mining and graph processing applications.