In this paper, a novel adequate and concise information extraction approach is explored to provide a promising alternative for manifesting the intrinsic structure of the cyclostationary signals, such as communication signals. A novel graph-based signal representation is proposed to interpret the spectral correlation function into a graph and its adjacency matrix. This graph can represent the proposed adequate and concise information about the communication signals in practice. A typical application, namely modulation classification, can be implemented using our proposed new graph-based approach. According to Monte Carlo simulation results, the proposed graph-based modulation classification method leads to the promising performance in both additive noise channels and difficult multipath fading channels, compared to other existing techniques also using the spectral correlation functions.