空间偏好依恋模型的几何图形特征
Geometric Graph Properties of the Spatial Preferred Attachment model
摘要：
空间偏好依恋（SPA）模型是一种网络化信息空间的模型，如万维网、引文图和在线社交网络。它使用一个度量空间来模拟顶点的隐藏属性。因此，顶点是度量空间的元素，链接的形成取决于顶点之间的度量距离。我们表明，通过理论分析和模拟，根据SPA模型形成的图，它是可以推断的度量顶点之间的距离从图的链接结构。准确地说，该估计是基于一对顶点的公共邻居的数量，一种称为{ \sl co-citation}的度量。为了能够计算出这个估计，我们推导出一个精确的关系的数量的共同邻居和度量距离。我们还分析了{ \sl边长}的分布，其中边长是其端点之间的度量距离。我们表明，这种分布有三个不同的制度，这种分布的尾部遵循幂律。
英文摘要：
The spatial preferred attachment (SPA) model is a model for networked information spaces such as domains of the World Wide Web, citation graphs, and on-line social networks. It uses a metric space to model the hidden attributes of the vertices. Thus, vertices are elements of a metric space, and link formation depends on the metric distance between vertices. We show, through theoretical analysis and simulation, that for graphs formed according to the SPA model it is possible to infer the metric distance between vertices from the link structure of the graph. Precisely, the estimate is based on the number of common neighbours of a pair of vertices, a measure known as {\sl co-citation}. To be able to calculate this estimate, we derive a precise relation between the number of common neighbours and metric distance. We also analyze the distribution of {\sl edge lengths}, where the length of an edge is the metric distance between its end points. We show that this distribution has three different regimes, and that the tail of this distribution follows a power law.
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