This paper presents the development of a new class of algorithms that accurately implement the preferential attachment mechanism of the Barab\'asi-Albert (BA) model to generate scale-free graphs. Contrary to existing approximate preferential attachment schemes, our methods are exact in terms of the proportionality of the vertex selection probabilities to their degree and run in linear time with respect to the order of the generated graph. Our algorithms are based on a principle of random sampling which is called whole sampling and is a new perspective for the study of preferential attachment. We show that they obey the definition of the original BA model that generates scale-free graphs and discuss their higher-order properties. Finally, we extend our analytical presentation with computer experiments that focus on the degree distribution and several measures surrounding the local clustering coefficient.

翻译：本文介绍了准确实施Barab\'asi-Albert(BA)模式优惠附加机制以生成无比例尺图的新型算法的发展情况,与现有的近似优惠附加方案相反,我们的方法精确地反映了顶顶选择概率的相称性,按生成图的顺序按其程度和线性时间计算。我们的算法基于随机抽样原则,称为整个抽样,是研究优惠附加物的新视角。我们表明它们遵守原始BA模式的定义,该模式生成无比例尺图表并讨论其较高顺序属性。最后,我们扩展了分析演示,以计算机实验为重点程度分布和围绕本地集聚系数的若干措施。