Centrality and power show important network structure characteristics of a major city. However, research on the city network often ignores the connection and the differences between these concepts. We explain the basic concepts underpinning both centrality and power. We introduce two concepts: recursive centrality and recursive power, to describe degree centrality and betweenness centrality as applied to a city's position and power in a network, respectively. We form a complete set of relational data based on a matching relationship between Chinese auto parts supply and demand in 2009. Finally we review China's urban network topology characteristics, such as node distribution and link relationships, and identify the relationship between the center and the power index. Empirical studies show that (1) the Chinese city network (based on auto parts supply and demand) is of low density, polycentric, and is characterized by the "rich club". (2) Shanghai, Changchun, Beijing, Chongqing and Shiyan show the highest level of centrality in their city networks within the six major auto industry regions (northeast China, Beijing-Tianjin, central China, Sichuan-Chongqing, and the Yangtze River Delta). (3) There are six major network power city clusters in China: the Yangtze River Delta, Beijing-Tianjin, Shandong Province, Guangxi autonomous region, Hubei Province, and Sichuan-Chongqing. Among them, the Yangtze River Delta is the most powerful one. (4) With regards to measuring centrality and power in a network, recursive centrality and recursive power are both discernible and accurate. (5) City network distribution features can be classified as either core cities, with high centrality and high power, or peripheral cities, with low centrality and low power. The damping effect of distance influences the degree of connection within a city. Other relationships exist, such as center city clusters, with high center and low power, and powerful gateway cities, with low centrality and high power.