Degree Correlation and Its Features of Spreading on Networks

There are multiple correlations in the connection of real-world networks, which have significant impact on topology, dynamical behavior of network, etc. Aiming at degree correlation, we propose a maximum weighted matching algorithm based on certain networks or degree sequence in order to construct networks with maximum and minimum degree correlation coefficient. And we analyze the relationship between network structure and degree correlation coefficient. Then we study the influence of mixing pattern on virus spreading such as spreading speed, threshold, and stable infected ratio, based on the networks with continuous correlation coefficient. Results show that disassortative network accelerates virus spreading while spread speed is more sensitive to assortative networks. Besides, study from the angle of immunization strategy indicates that the strategies that aim at nodes with higher degree are more efficient for disassortative networks. While in real condition, the immunization should be comprehensively considered according to the effective infected ratio, correlation coefficient, objective of immunization and so on.