Emergence of disassortative/assortative mixing pattern and generative model

      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. Besides, we comprehensively analyze the degree correlation of randomly rewired scale-free networks and show that random rewiring increases disassortativity by reducing the average degree of the nearest neighbors of high-degree nodes. The effect can be captured by the measures of the degree correlation that consider all links in the network, but not by analogous measures that consider only links between degree peers, hence the potential for contradicting interpretations. We furthermore find that random and directional rewiring affect the topology of a scale-free network differently, even if the degree correlation of the rewired networks is the same.