论文标题
对优先附件网络中平均场近似的批评
A critique of the Mean Field Approximation in preferential attachment networks
论文作者
论文摘要
平均场近似（MFA）或连续方法通常在网络上的课程中使用，以得出优先附件网络的程度分布。此方法很简单，结果接近正确的答案。但是，本文表明该方法在几个方面存在缺陷，从而导致无法解决的矛盾。更重要的是，MFA不是明确源自数学模型的。对隐含模型的分析表明，它的近似值远非事实，而另一个则无法动机。因此，MFA对于优先依恋网络的成功是偶然的，该方法不适合教学本科生。
The Mean Field Approximation (MFA), or continuum method, is often used in courses on Networks to derive the degree distribution of preferential attachment networks. This method is simple and the outcome is close to the correct answer. However, this paper shows that the method is flawed in several aspects, leading to unresolvable contradictions. More importantly, the MFA is not explicitly derived from a mathematical model. An analysis of the implied model shows that it makes an approximation which is far from the truth and another one which can not be motivated in general. The success of the MFA for preferential attachment networks is therefore accidental and the method is not suitable for teaching undergraduates.
