Local Weak Convergence Based Analysis of a New Graph Model

Mehrdad Moharrami, V. Subramanian, M. Liu, R. Sundaresan
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Abstract

Different random graph models have been proposed as an attempt to model individuals’ behavior. Each of these models proposes a unique way to construct a random graph that covers some properties of the real-world networks. In a recent work [4], the proposed model tries to capture the self-optimizing behavior of the individuals in which the links are made based on the cost/benefit of the connection. In this paper, we analyze the asymptotics of this graph model. We prove the model locally weakly converges [1] to a rooted tree associated with a branching process which we named Erlang Weighted Tree(EWT) and analyze the main properties of the EWT.
基于局部弱收敛的新图模型分析
人们提出了不同的随机图模型,试图对个体的行为进行建模。这些模型中的每一个都提出了一种独特的方法来构建一个随机图,该图涵盖了现实世界网络的一些属性。在最近的一项研究[4]中,提出的模型试图捕捉个体的自我优化行为,在这种行为中,连接是基于连接的成本/收益建立的。本文分析了该图模型的渐近性。我们证明了该模型局部弱收敛[1]到一个与分支过程相关的根树,我们将其命名为Erlang加权树(EWT),并分析了EWT的主要性质。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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