摘要翻译：
为了研究复杂网络上的实际运输现象，我们分析了一个由大约100万家日本公司组成的公司间贸易网络的经验数据，以及这些公司的销售额（一笔销售额对应于一个节点的总流入）。首先，我们分析了销售额与最近邻的销售额之间的关系，由此我们得到了销售额与最近邻（即顾客）销售额的加权和之间的简单线性关系。此外，我们引入了一个简单的货币运输模型，这是一致的经验观察。在这个模型中，一个公司（即顾客）将钱按目的地的比例分配给它的边缘（供应商）。通过深入的数值模拟，我们发现由这些模型导出的稳定流可以近似地再现实际企业的销售分布。从货币运输模型推导出的单个公司的销售额平均与实际销售额成正比。
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英文标题：
《Biased diffusion on Japanese inter-firm trading network: Estimation of
  sales from network structure》
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作者：
Hayafumi Watanabe, Hideki Takayasu, Misako Takayasu
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最新提交年份：
2011
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：General Finance        一般财务
分类描述：Development of general quantitative methodologies with applications in finance
通用定量方法的发展及其在金融中的应用
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一级分类：Computer Science        计算机科学
二级分类：Social and Information Networks        社会和信息网络
分类描述：Covers the design, analysis, and modeling of social and information networks, including their applications for on-line information access, communication, and interaction, and their roles as datasets in the exploration of questions in these and other domains, including connections to the social and biological sciences. Analysis and modeling of such networks includes topics in ACM Subject classes F.2, G.2, G.3, H.2, and I.2; applications in computing include topics in H.3, H.4, and H.5; and applications at the interface of computing and other disciplines include topics in J.1--J.7. Papers on computer communication systems and network protocols (e.g. TCP/IP) are generally a closer fit to the Networking and Internet Architecture (cs.NI) category.
涵盖社会和信息网络的设计、分析和建模，包括它们在联机信息访问、通信和交互方面的应用，以及它们作为数据集在这些领域和其他领域的问题探索中的作用，包括与社会和生物科学的联系。这类网络的分析和建模包括ACM学科类F.2、G.2、G.3、H.2和I.2的主题；计算应用包括H.3、H.4和H.5中的主题；计算和其他学科接口的应用程序包括J.1-J.7中的主题。关于计算机通信系统和网络协议（例如TCP/IP）的论文通常更适合网络和因特网体系结构（CS.NI）类别。
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一级分类：Physics        物理学
二级分类：Physics and Society        物理学与社会
分类描述：Structure, dynamics and collective behavior of societies and groups (human or otherwise). Quantitative analysis of social networks and other complex networks. Physics and engineering of infrastructure and systems of broad societal impact (e.g., energy grids, transportation networks).
社会和团体（人类或其他）的结构、动态和集体行为。社会网络和其他复杂网络的定量分析。具有广泛社会影响的基础设施和系统（如能源网、运输网络）的物理和工程。
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英文摘要：
  To investigate the actual phenomena of transport on a complex network, we analysed empirical data for an inter-firm trading network, which consists of about one million Japanese firms and the sales of these firms (a sale corresponds to the total in-flow into a node). First, we analysed the relationships between sales and sales of nearest neighbourhoods from which we obtain a simple linear relationship between sales and the weighted sum of sales of nearest neighbourhoods (i.e., customers). In addition, we introduce a simple money transport model that is coherent with this empirical observation. In this model, a firm (i.e., customer) distributes money to its out-edges (suppliers) proportionally to the in-degree of destinations. From intensive numerical simulations, we find that the steady flows derived from these models can approximately reproduce the distribution of sales of actual firms. The sales of individual firms deduced from the money-transport model are shown to be proportional, on an average, to the real sales.
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PDF链接：
https://arxiv.org/pdf/1111.4852