  Air pollution has become a major issue and caused widespread environmental
and health problems. Aerosols or particulate matters are an important component
of the atmosphere and can transport under complex meteorological conditions.
Based on the data of $PM_{2.5}$ observations, we develop a network approach to
study and quantify their spreading and diffusion patterns. We calculate
cross-correlation functions of time lag between sites within different season.
The probability distribution of correlation changes with season. It is found
that the probability distributions in four seasons can be scaled into one
scaling function with averages and standard deviations of correlation. This
seasonal scaling behavior indicates there is the same mechanism behind
correlations of $PM_{2.5}$ concentration in different seasons. Further, from
weighted and directional degrees of complex network, different properties of
$PM_{2.5}$ concentration are studied. The weighted degrees reveal the strongest
correlations of $PM_{2.5}$ concentration in winter and in the North China
plain. These directional degrees show net influences of $PM_{2.5}$ along Gobi
and inner Mongolia, the North China plain, Central China, and Yangtze River
Delta.
