生长网络度分布头部的刻画
Characterizing the head of the degree distributions of growing networks
摘要：
本文的分析有助于解释度分布遵循扩展指数或幂律尾部的增长网络的形成。我们提出了一个通用的模型，在该模型中，边缘动态驱动的新节点的连续附件和混合附件机制，触发随机或优先附件。此外，根据响应机制建立到新添加的节点的互逆边。建议的框架扩展了以前的混合附件模型，允许新的边缘的数量根据不同的离散概率分布，包括泊松，二项式，泽塔，对数系列。我们推导出解析表达式的限制度分布，结果从混合的附件和响应机制。此外，我们描述的累积度分布的动态演化。仿真结果说明了新边的数量和互易过程如何显著影响度分布的头部。
英文摘要：
The analysis in this paper helps to explain the formation of growing networks with degree distributions that follow extended exponential or power-law tails. We present a generic model in which edge dynamics are driven by a continuous attachment of new nodes and a mixed attachment mechanism that triggers random or preferential attachment. Furthermore, reciprocal edges to newly added nodes are established according to a response mechanism. The proposed framework extends previous mixed attachment models by allowing the number of new edges to vary according to various discrete probability distributions, including Poisson, Binomial, Zeta, and Log-Series. We derive analytical expressions for the limit in-degree distribution that results from the mixed attachment and response mechanisms. Moreover, we describe the evolution of the dynamics of the cumulative in-degree distribution. Simulation results illustrate how the number of new edges and the process of reciprocity significantly impact the head of the degree distribution.
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