It is well known that dynamical processes on complex networks are influenced by the degree correlations. A common way to take these into account in a mean-field approach is to consider the function $k_{nn}\left(k\right)$ (average nearest neighbors degree). We re-examine the standard choices of $k_{nn}$ for scale-free networks and a new family of functions which is independent from the simple ansatz $k_{nn}\propto k^{\alpha }$ but still displays a remarkable scale invariance. A rewiring procedure is then used to explicitely construct synthetic networks using the full correlation $P\left(h\right|k)$ from which $k_{nn}$ is derived. We consistently find that the $k_{nn}$ functions of concrete synthetic networks deviate from ideal assortativity or disassortativity at large k. The consequences of this deviation on a diffusion process (the network Bass diffusion and its peak time) are numerically computed and discussed for some low-dimensional samples. Finally, we check that although the $k_{nn}$ functions of the new family have an asymptotic behavior for large networks different from previous estimates, they satisfy the general criterium for the absence of an epidemic threshold.

中文翻译：

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均值场方法与综合相关网络的仿真比较

众所周知，复杂网络上的动力学过程受程度相关性的影响。在均值场方法中考虑这些因素的常见方法是考虑函数${ķ}_{ññ}（ķ）$（平均最近邻居度）。我们重新检查的标准选择${ķ}_{ññ}$ 适用于无标度网络和独立于简单ansatz的新功能系列 ${ķ}_{ññ}\propto {ķ}^{\alpha }$但仍然显示出明显的尺度不变性。然后使用重新布线过程使用完全相关性显式构建合成网络$P（H|ķ）$ 从中 ${ķ}_{ññ}$派生。我们始终发现${ķ}_{ññ}$在k较大时，混凝土合成网络的功能偏离了理想的可分解性。对于一些低维样本，通过数值计算并讨论了这种偏差对扩散过程（网络低音扩散及其峰值时间）的影响。最后，我们检查了${ķ}_{ññ}$ 新家族的功能对于不同于先前估计的大型网络具有渐近行为，它们满足了没有流行阈值的一般标准。