Air quality impacts people's health and daily life, affects the sensitive ecosystems, and even restrains a country's development. By collecting and processing the time series data of Air Quality Index (AQI) of 363 cities of China from Jan. 2015 to Mar. 2019, we dedicated to characterize the universal patterns, the clustering and correlation of air quality of different cities by using the methods of complex network and time series analysis. The main results are as follows: 1) The Air Quality Network of China (AQNC) is constructed by using the Planar Maximally Filtered Graph (PMFG) method. The geographical distances on the correlation of air quality of different cities have been studied, it is found that 100 km is a critical distance for strong correlation. 2) Seven communities of AQNC have been detected, and their patterns have been analyzed by taking into account the Hurst exponent and climate environment, it is shown that the seven communities are reasonable, and they are significantly influenced by the climate factors, such as monsoon, precipitation, geographical regions, etc. 3) The motifs of air quality time series of seven communities have been investigated by the visibility graph, for some communities, the evolutionary patterns of the motifs are a bit stable, and they have the long-term memory effects. While for others, there are no stable patterns.