利用邻域可拓性诱导网络玩具模型的自组织临界性
Inducing Self-Organized Criticality in a network toy model by neighborhood assortativity
摘要：
复杂网络是近年来出现的一种研究复杂系统的框架，它包括自组织临界性（SOC）等。网络节点倾向于链接到其他类似类型的节点，其特征在于连续混合。真实网络表现出顶点度的混合，然而典型的随机网络模型，如Erdos-Renyi或Barabasi-Albert，没有表现出任何混合。在本文中，我们介绍了邻域的非线性概念，作为一个节点的倾向，属于一个社区（它的邻居），显示出类似于自己的平均属性。在一个网络玩具模型中，通过引入邻域的按度随机混合，可以发现SOC的动态性，并通过涨落分析表征了由临界性引起的长程相关性，表明节点的活动性与临界性之间存在着线性关系。该模型仅包含一个参数，其不同参数值的统计图可以折叠成一条曲线。该模型的简单性允许进行数值模拟，也可以分析研究的统计参数的特定值，利用马尔可夫链。
英文摘要：
Complex networks are a recent type of frameworks used to study complex systems with many interacting elements, such as Self-Organized Criticality (SOC). The network node's tendency to link to other nodes of similar type is characterized by assortative mixing. Real networks exhibit assortative mixing by vertex degree, however typical random network models, such as Erdos-Renyi or Barabasi-Albert, show no assortative arrangements. In this paper we introduce the neighborhood assortativity notion, as the tendency of a node to belong to a community (its neighborhood) showing an average property similar to its own. Imposing neighborhood assortative mixing by degree in a network toy model, SOC dynamics can be found. The long-range correlations resulting from the criticality have been characterized by means of fluctuation analysis and show an anticorrelation in the node's activity. The model contains only one parameter and its statistics plots for different values of the parameter can be collapsed into a single curve. The simplicity of the model allows performing numerical simulations and also to study analytically the statistics for a specific value of the parameter, making use of the Markov chains.
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