A reduced condition for liquid-gas phase transition from the singularity of compressibility is derived using diagrammatic approach and is examined in the hard sphere system. The condition turns out that the Percus-Yevick and the Hyper-Netted-Chain approximation never conceive the idea of phase transition, and explains that the liquid-gas transition does not exist in hard sphere system. The solid-fluid transition is considered on the viewpoint of correlation function and diagrammatic analysis.