Epidemic spreading on undirected and directed scale-free networks with   correlations
  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. 
Yukio Hayashi