We develop the linear response theory for the Google matrix PageRank algorithm with respect to a general weak perturbation and a numerical efficient and accurate algorithm, called LIRGOMAX algorithm, to compute the linear response of the PageRank with respect to this perturbation. We illustrate its efficiency on the example of the English Wikipedia network with more than 5 millions of articles (nodes). For a group of initial nodes (or simply a pair of nodes) this algorithm allows to identify the effective pathway between initial nodes thus selecting a particular subset of nodes which are most sensitive to the weak perturbation applied to them (injection or pumping at one node and absorption of probability at another node). The further application of the reduced Google matrix algorithm (REGOMAX) allows to determine the effective interactions between the nodes of this subset. General linear response theory already found numerous applications in various areas of science including statistical and mesoscopic physics. Based on these grounds we argue that the developed LIRGOMAX algorithm will find broad applications in the analysis of complex directed networks.
We use the United Nations COMTRADE database for analysis of the multiproduct world trade network. With this data, considered for years 2012-2018, we determined the world trade impact of the Kernel of EU 9 countries (KEU9), being Austria, Belgium, France, Germany, Italy, Luxembourg, Netherlands, Portugal, Spain, considered as one united country. We apply the advanced Google matrix analysis for investigation of the influence of KEU9 and show that KEU9 takes the top trade network rank positions thus becoming the main player of the world trade being ahead of USA and China. Our network analysis pro…
Interactions and influence of world painters from the reduced Google matrix of Wikipedia networks
本研究的目的是从维基百科的网络结构中提取绘画艺术史知识。因此，我们构建了代表7个维基百科语言版本的文章的超链接结构的网页的理论网络。这7个网络进行分析，以提取最有影响力的画家在每个版本使用谷歌矩阵理论。使用PageRank算法测量了3000多名画家的网页重要性。最有影响力的画家被招募，他们的关系进行了研究，减少谷歌矩阵分析。Reduced Google Matrix是一种强大的方法，它可以捕获选定节点子集之间的直接和隐藏交互，同时考虑到这些节点之间通过大型全球网络的其余部分的间接链接。该方法起源于核物理和介观物理的散射理论以及量子混沌领域。从这项研究中，我们表明，它是可以从减少谷歌矩阵的组件提取有意义的信息，这些画家之间的关系。例如，我们的分析将属于同一绘画运动的画家分组，并显示不同运动的画家之间有意义的联系。我们还使用维基百科上有关画家和国家的文章之间的链接敏感度来确定画家对世界各国的影响。简化的Google矩阵方法允许获得维基百科语言版本的各种文化观点的平衡视图。在维基百科的七个版本中，拥有最多顶级画家的国家是意大利、法国和俄罗斯。我们认为，这种方法提供了关于艺术的有意义的信息，它可以成为人类知识和文化的广泛网络分析的一部分。
In past ten years, modern societies developed enormous communication and social networks. Their classification and information retrieval processing become a formidable task for the society. Due to the rapid growth of World Wide Web, social and communication networks, new mathematical methods have been invented to characterize the properties of these networks on a more detailed and precise level. Various search engines are essentially using such methods. It is highly important to develop new tools to classify and rank enormous amount of network information in a way adapted to internal network s…
In the literature about web survey methodology, significant efforts have been made to understand the role of time-invariant factors (e.g. gender, education and marital status) in (non-)response mechanisms. Time-invariant factors alone, however, cannot account for most variations in (non-)responses, especially fluctuations of response rates over time. This observation inspires us to investigate the counterpart of time-invariant factors, namely time-varying factors and the potential role they play in web survey (non-)response. Specifically, we study the effects of time, weather and societal tren…
我们使用联合国商品贸易统计数据库[http：//comtrade.un.org/db/]构建了世界贸易网络的Google矩阵，并分析了1962年至2009年所有国家和所有可用年份的各种贸易商品的特性。该网络上的贸易流进行分类的帮助下，PageRank和CheiRank算法开发的万维网和其他大规模的有向网络。对于世界贸易来说，这一排名在平等的民主基础上对待所有国家，而不考虑国家的富裕程度。这种方法仍然使一组工业发达国家在{ \it all commodities}的贸易中名列前茅。我们的研究建立了存在两个固态的富国和穷国，保持稳定的时间域，而大多数国家被证明是在一个类似气体的阶段与强大的秩波动。一个简单的随机矩阵模型可以很好地描述二维等级平面上国家的统计分布。与通常的出口和进口排名的比较突出了我们的方法的新功能和可能性。
We develop the Google matrix analysis of the multiproduct world trade network obtained from the UN COMTRADE database in recent years. The comparison is done between this new approach and the usual Import-Export description of this world trade network. The Google matrix analysis takes into account the multiplicity of trade transactions thus highlighting in a better way the world influence of specific countries and products. It shows that after Brexit, the European Union of 27 countries has the leading position in the world trade network ranking, being ahead of USA and China. Our approach determ…
Using the United Nations Comtrade database, we perform the Google matrix analysis of the multiproduct World Trade Network (WTN) for the years 2018-2020 comprising the emergence of the COVID-19 as a global pandemic. The applied algorithms -- the PageRank, the CheiRank and the reduced Google matrix -- take into account the multiplicity of the WTN links providing new insights on the international trade comparing to the usual import-export analysis. These algorithms establish new rankings and trade balances of countries and products considering every countries on equal grounds, independently of th…
