A network is scale-free if its connectivity density function is proportional to a power-law distribution. It has been suggested that scale-free networks may provide an explanation for the robustness observed in certain physical and biological phenomena, since the presence of a few highly connected hub nodes and a large number of small-degree nodes may provide alternate paths between any two nodes on average-such robustness has been suggested in studies of metabolic networks, gene interaction networks and protein folding. A theoretical justification for why many networks appear to be scale-free has been provided by Barabási and Albert, who argue that expanding networks, in which new nodes are preferentially attached to highly connected nodes, tend to be scale-free. In this paper, we provide the first efficient algorithm to compute the connectivity density function for the ensemble of all homopolymer secondary structures of a user-specified length-a highly nontrivial result, since the exponential size of such networks precludes their enumeration. Since existent power-law fitting software, such as powerlaw, cannot be used to determine a power-law fit for our exponentially large RNA connectivity data, we also implement efficient code to compute the maximum likelihood estimate for the power-law scaling factor and associated Kolmogorov-Smirnov p value. Hypothesis tests strongly indicate that homopolymer RNA secondary structure networks are not scale-free; moreover, this appears to be the case for real (non-homopolymer) RNA networks.

中文翻译：

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RNA网络是无尺度的吗？

如果网络的连通性密度函数与幂律分布成比例，则它是无标度的。有人提出，无标度网络可以为某些物理和生物学现象中观察到的鲁棒性提供解释，因为存在几个高度连接的集线器节点和大量小角度节点可以在任何两个之间提供替代路径。在代谢网络，基因相互作用网络和蛋白质折叠的研究中已经提出了平均而言这样的鲁棒性。Barabási和Albert提出了为什么许多网络似乎是无标度的理论依据，他们认为扩展网络（其中新节点优先连接到高度连接的节点）往往是无标度的。在本文中，我们提供了第一种有效的算法来计算用户指定长度的所有均聚物二级结构的集合的连接密度函数，这是一个非常重要的结果，因为此类网络的指数大小无法对其进行枚举。由于无法使用现有的幂律拟合软件（例如powerlaw）来确定我们的指数较大的RNA连接数据的幂律拟合，因此我们还实现了有效的代码，以计算幂律缩放因子及其相关的最大似然估计Kolmogorov-Smirnov p值。假设检验强烈表明，均聚物RNA二级结构网络并非无标度。此外，对于真实的（非均聚物）RNA网络来说似乎是这种情况。