Technological advancements in the current era of big data have led to rapid generation and collection of very large amounts of valuable data from a wide variety of rich data sources. As rich data sources, social networks consist of social entities that are linked by some social relationships (e.g., kinship, colleagueship, co-authorship, friendship, followship). Usually, these networks are very big but also very sparse. Embedded in the very sparse but very big networks are implicit, previously unknown and potentially useful information and knowledge that can be discovered by social network analysis and mining. In this paper, we aim to discover interesting social relationships from very sparse but very big social network data. Due to the sparsity of the data, we effectively compress bitmaps representing social entities in the data, from which useful information can be mined and interesting knowledge can be discovered. Evaluation results show the effectiveness of our compression scheme for very sparse but very big social network data.