In the hydrogen network with the minimum hydrogen utility flow rate, the pinch appears at the point with zero hydrogen surplus, while the hydrogen surpluses of all the other points are positive. In the hydrogen purity profiles, the pinch can only lie at the sink-tie-line intersecting the source purity profile. According to the alternative distribution of the negative and positive regions, the effect of the purification to the hydrogen surplus is analyzed. The results show that when the purification is applied, the pinch point will appear neither above the purification feed nor between the initial pinch point and the purification feed, no matter the purification feed lies above or below the initial pinch point. This is validated by two case studies.