论文标题
优先依恋与健身依赖性选择
Preferential attachment with fitness dependent choice
论文作者
论文摘要
我们研究了不断发展的树模型中最大程度的渐近行为，并根据顶点的程度和适应性进行了选择。树是以以下递归方式构造的。为每个顶点分配一个参数，称为顶点的适合度。我们从两个顶点和它们之间的边缘开始。在每个步骤中，我们都会考虑一个重复的样本，重复$ d $顶点，以与其度成正比的概率和一些参数$β> -1 $选择。然后，我们添加了一个新的顶点，并从其具有最高的健身和程度产物的样品中将边缘从其到顶点。我们证明取决于模型的参数，最大程度可以表现出三种类型的渐近行为：sublinear，linear和$ n/\ ln n $顺序，其中$ n $是图中的边缘数。
We study the asymptotic behavior of the maximum degree in the evolving tree model with a choice based on both degree and fitness of a vertex. The tree is constructed in the following recursive way. Each vertex is assigned a parameter to it that is called a fitness of a vertex. We start from two vertices and an edge between them. On each step we consider a sample with repetition of $d$ vertices, chosen with probabilities proportional to their degrees plus some parameter $β>-1$. Then we add a new vertex and draw an edge from it to the vertex from the sample with the highest product of fitness and degree. We prove that dependent on parameters of the model, the maximum degree could exhibit three types of asymptotic behavior: sublinear, linear and of $n/\ln n$ order, where $n$ is the number of edges in the graph.
