Lee Sang Hoon, Cucuringu Mihai, Porter Mason A
Oxford Centre for Industrial and Applied Mathematics, Mathematical Institute, University of Oxford, Oxford OX2 6GG, United Kingdom.
Program in Applied and Computational Mathematics (PACM), Princeton University, Fine Hall, Washington Road, Princeton, New Jersey 08544-1000, USA and Department of Mathematics, University of California, Los Angeles, Los Angeles, California 90095, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Mar;89(3):032810. doi: 10.1103/PhysRevE.89.032810. Epub 2014 Mar 20.
Networks often possess mesoscale structures, and studying them can yield insights into both structure and function. It is most common to study community structure, but numerous other types of mesoscale structures also exist. In this paper, we examine core-periphery structures based on both density and transport. In such structures, core network components are well-connected both among themselves and to peripheral components, which are not well-connected to anything. We examine core-periphery structures in a wide range of examples of transportation, social, and financial networks-including road networks in large urban areas, a rabbit warren, a dolphin social network, a European interbank network, and a migration network between counties in the United States. We illustrate that a recently developed transport-based notion of node coreness is very useful for characterizing transportation networks. We also generalize this notion to examine core versus peripheral edges, and we show that the resulting diagnostic is also useful for transportation networks. To examine the properties of transportation networks further, we develop a family of generative models of roadlike networks. We illustrate the effect of the dimensionality of the embedding space on transportation networks, and we demonstrate that the correlations between different measures of coreness can be very different for different types of networks.
网络通常具有中尺度结构，对其进行研究能够深入了解结构与功能。研究社区结构最为常见，但也存在许多其他类型的中尺度结构。在本文中，我们基于密度和传输来研究核心 - 外围结构。在这类结构中，核心网络组件自身之间以及与外围组件之间连接良好，而外围组件与其他任何组件的连接都不佳。我们在广泛的交通、社会和金融网络示例中研究核心 - 外围结构，包括大城市地区的道路网络、兔穴、海豚社交网络、欧洲银行同业网络以及美国各县之间的移民网络。我们表明，最近开发的基于传输的节点核心度概念对于刻画交通网络非常有用。我们还将这一概念进行推广以研究核心与外围边，并且表明所得诊断对于交通网络也很有用。为了进一步研究交通网络的特性，我们开发了一类类似道路网络的生成模型。我们说明了嵌入空间维度对交通网络的影响，并且证明了对于不同类型的网络，不同核心度度量之间的相关性可能非常不同。
