Sheridan Paul, Onodera Taku
Department of Active Life Promotion Science, Hirosaki University, Hirosaki, 036-8562, Japan.
The University of Tokyo, Institute of Medical Science, Human Genome Center, Tokyo, 108-8639, Japan.
Sci Rep. 2018 Feb 12;8(1):2811. doi: 10.1038/s41598-018-21133-2.
Every network scientist knows that preferential attachment combines with growth to produce networks with power-law in-degree distributions. How, then, is it possible for the network of American Physical Society journal collection citations to enjoy a log-normal citation distribution when it was found to have grown in accordance with preferential attachment? This anomalous result, which we exalt as the preferential attachment paradox, has remained unexplained since the physicist Sidney Redner first made light of it over a decade ago. Here we propose a resolution. The chief source of the mischief, we contend, lies in Redner having relied on a measurement procedure bereft of the accuracy required to distinguish preferential attachment from another form of attachment that is consistent with a log-normal in-degree distribution. There was a high-accuracy measurement procedure in use at the time, but it would have have been difficult to use it to shed light on the paradox, due to the presence of a systematic error inducing design flaw. In recent years the design flaw had been recognised and corrected. We show that the bringing of the newly corrected measurement procedure to bear on the data leads to a resolution of the paradox.
每位网络科学家都知道，偏好依附与网络增长相结合会产生具有幂律入度分布的网络。那么，当美国物理学会期刊论文引用网络被发现是按照偏好依附方式增长时，它为何会呈现对数正态引用分布呢？这个异常结果，我们将其称为偏好依附悖论，自物理学家西德尼·雷德纳十多年前首次提及以来，一直没有得到解释。在此我们提出一种解决方案。我们认为，问题的主要根源在于雷德纳所依赖的测量方法缺乏区分偏好依附与另一种与对数正态入度分布相符的依附形式所需的精度。当时有一种高精度测量方法在使用，但由于存在导致设计缺陷的系统误差，很难用它来阐明这个悖论。近年来，这个设计缺陷已被识别并纠正。我们表明，将新修正的测量方法应用于这些数据可解决该悖论。
