论文标题
不断发展的网络的极端特性：局部依赖和重型尾巴
Extremal properties of evolving networks: local dependence and heavy tails
论文作者
论文摘要
在随机图中使用了具有预测的尾部和极端指标的网络演化以及用作节点影响指标的最大线性模型。尾部指数显示出分配尾部的重度。极端指数是随机过程的聚类（或局部依赖性）的量度。该群集意味着在足够高的阈值上连续超出该过程的一组。我们的最新结果有关定期变化随机变量的非平稳随机长度序列的总和和最大值扩展到随机图。从一组连接的固定种子群落作为热点开始，并将其对其尾部索引，可以确定附加到网络的新节点的尾巴和极端指标进行排名。此过程使我们能够通过尾巴和极端指数来预测时间网络的演变。极端指数确定了PageRank的最大值和新连接节点的最大线性模型的限制分布。博览会由算法和示例提供。为了验证我们的理论结果，我们提供了有关线性优先附着作为网络增长工具的模拟和实际数据研究。
A network evolution with predicted tail and extremal indices of PageRank and the Max-Linear Model used as node influence indices in random graphs is considered. The tail index shows a heaviness of the distribution tail. The extremal index is a measure of clustering (or local dependence) of the stochastic process. The cluster implies a set of consecutive exceedances of the process over a sufficiently high threshold. Our recent results concerning sums and maxima of non-stationary random length sequences of regularly varying random variables are extended to random graphs. Starting with a set of connected stationary seed communities as a hot spot and ranking them with regard to their tail indices, the tail and extremal indices of new nodes that are appended to the network may be determined. This procedure allows us to predict a temporal network evolution in terms of tail and extremal indices. The extremal index determines limiting distributions of a maximum of the PageRank and the Max-Linear Model of newly attached nodes. The exposition is provided by algorithms and examples. To validate our theoretical results, our simulation and real data study concerning a linear preferential attachment as a tool for network growth are provided.
