To enable lossless compression, an auxiliary bitmap is used to provide side information about the graph bitmap. Each bit in the auxiliary bitmap represents a word in the graph bitmap. A zero bit in the auxiliary bitmap means that the corresponding word in the graph bitmap is not transmitted. Therefore, it is set to the default value, λ, during decompression. This default value could be either an all-zeros word, or all-ones word depending on the BFS step. A one bit in the auxiliary bitmap means that the corresponding word in the graph bitmap is transmitted.