The rapid development of Internet technology has strengthened the information connection between cities and resulted in the continuous restructuring of its spatial structure. According to the Baidu index data between cities in 2012 and 2019, social network and spatial analyses were performed at local and national scales to investigate the spatiotemporal evolution pattern of the urban network in the Yellow River Basin of China. The findings revealed the following: (1) Urban degree centrality at the national scale is highly correlated with that at the local scale. However, compared with the local scale, cities with high-value degree centrality are concentrated in the east, which increases spatial disequilibrium, and the positions of Xi’an City and Qingdao City in the network are prominent. (2) Urban betweenness centrality at the national scale is not related to that at the local scale. Cities with high-value betweenness centrality shift from west to east, and the spatial disequilibrium is low. Furthermore, the intermediary effect of Xi’an City is prominent. (3) The internal connection network presents two mutual isolated backbone networks centered on Xi’an-Zhengzhou Cities and Qingdao-Jinan Cities, and the high-level connections outside the basin are increasingly located in the Yangtze River Delta, Chengdu-Chongqing, and other southern urban agglomerations. (4) Compared with the local scale, the spatial organization of the first contact exhibits limited change at the national scale, and the second contact urban nodes have mostly converted from the basin center or provincial subcenter to Beijing City. The third contact urban nodes have mostly converted from the neighboring nodes to national centers outside the basin. This study can be a reference for the cooperative promotion of high-quality development in the Yellow River Basin.