Emergence of disassortative mixing from pruning nodes in growing scale-free networks.

Abstract

Disassortative mixing is ubiquitously found in technological and biological networks, while the corresponding interpretation of its origin remains almost virgin. We here give evidence that pruning the largest-degree nodes of a growing scale-free network has the effect of decreasing the degree correlation coefficient in a controllable and tunable way, while keeping both the trait of a power-law degree distribution and the main properties of network's resilience and robustness under failures or attacks. The essence of these observations can be attributed to the fact the deletion of large-degree nodes affects the delicate balance of positive and negative contributions to degree correlation in growing scale-free networks, eventually leading to the emergence of disassortativity. Moreover, these theoretical prediction will get further validation in the empirical networks. We support our claims via numerical results and mathematical analysis, and we propose a generative model for disassortative growing scale-free networks.