Graph contrastive learning has improved graph representation learning, becoming a successful unsupervised graph representation learning method. This method first generates two or more views of the input graph through data augmentation and learns node representations by maximizing the consistency between views. However, existing methods mostly use random data augmentation strategies, such as randomly deleting edges and randomly masking features, or ignore the rich global information in the graph structure, resulting in poor performance. This paper proposes a new unsupervised graph contrastive learning with higher-order networks (GCH). Since data augmentation is a key component of contrastive learning, this paper introduces high-order networks by incorporating similarity-based global information into the original graph. Then, a method combining adaptive and random enhancement strategies is used to make the semantic information between the two graph views complementary, preserving important semantic information while avoiding excessive similarity. In addition, the previous methods only consider the same nodes as positive samples, and this paper identifies positive samples based on capturing global information. Extensive experiments on eight public graph benchmark datasets show that the GCH algorithm outperforms existing state-of-the-art algorithms in node classification tasks, even surpassing supervised learning algorithms.