A striking discovery in the field of network science is that the majority of real networked systems have some universal structural properties. In generally, they are simultaneously sparse, scale-free, small-world, and loopy. In this paper, we investigate the second-order consensus of dynamic networks with such universal structures subject to white noise at vertices. We focus on the network coherence $H_{\rm SO}$ characterized in terms of the $\mathcal{H}_2$-norm of the vertex systems, which measures the mean deviation of vertex states from their average value. We first study numerically the coherence of some representative real-world networks. We find that their coherence $H_{\rm SO}$ scales sublinearly with the vertex number $N$. We then study analytically $H_{\rm SO}$ for a class of iteratively growing networks -- pseudofractal scale-free webs (PSFWs), and obtain an exact solution to $H_{\rm SO}$, which also increases sublinearly in $N$, with an exponent much smaller than 1. To explain the reasons for this sublinear behavior, we finally study $H_{\rm SO}$ for Sierpin\'ski gaskets, for which $H_{\rm SO}$ grows superlinearly in $N$, with a power exponent much larger than 1. Sierpin\'ski gaskets have the same number of vertices and edges as the PSFWs, but do not display the scale-free and small-world properties. We thus conclude that the scale-free and small-world, and loopy topologies are jointly responsible for the observed sublinear scaling of $H_{\rm SO}$.

翻译：在网络科学领域,一个惊人的发现是,大多数真正的网络系统都具有一些普遍性的结构特性。一般来说,它们同时是分散的、无规模的、小世界的和循环的。在本文中,我们调查了具有这种普遍性结构的动态网络的第二级共识,这些网络在脊椎上受到白色噪音的影响。我们集中研究网络一致性$H ⁇ rm SO}美元,其特点是顶端系统美元=mathcal{H ⁇ 2美元-norm,该等值测量了顶端国家的平均值的偏差。我们首先从数字上研究一些具有代表性的实际世界网络的连贯性。我们发现,这些网络的连贯性是美元SO+rmSO的相对规模。我们然后分析一下,对于一个迭代不断增长的网络,即假的无规模网络(PSFWs)美元,其精确的答案是 $HrmSOSF}, 其次线以美元为基底线, 其显示的比1美元要小,其显示的数值要小得多。