How can we accurately classify graphs using only positive and unlabeled instances? This setting commonly arises in real-world tasks. For example, in drug side effect prediction, each drug is represented as a graph based on its chemical structure, and only those observed to cause adverse effects are labeled as positive. The remaining drugs are left unlabeled—not because they are confirmed safe, but because such side effects have not yet been discovered or reported. A challenge is that positive and negative graphs often share similar substructures, making it difficult for models to capture the subtle structural differences that distinguish true positives among unlabeled ones. This difficulty is further exacerbated by the absence of explicit negative labels, which leaves the model without clear guidance on how to separate informative from non-informative patterns. We propose Delta-PU, an accurate method for PU graph classification. Delta-PU performs dual reweighting: hop-level reweighting to emphasize informative substructures during pooling, and graph-level reweighting to suppress ambiguous unlabeled graphs. This dual mechanism allows the model to progressively focus on discriminative patterns while reducing the uncertainty introduced by unlabeled instances. Extensive experiments demonstrate that Delta-PU achieves the state-of-the-art performance in PU graph classification.