  Scale-free (SF) network structures observed in many complex systems affect
the size of epidemic spreading and the efficiency of communication, statistical
properties of the degree-degree correlations are important for studying the
average behavior. We numerically investigate the epidemic behavior on
evolutional SF network models with parametrically varied correlations between
the assortative, uncorrelated, and disassortative. According to the types of
correlations, different behavior is found in particular for a directed model.
Our results suggest that the spreading is more enhanced by assortative
connections between nodes with similar degrees rather than by uncorrelated or
disassortative ones between cooperative nodes with high and low degrees.
