Community Structure In Multislice Networks

网络科学，研究相互连接的实体及其功能相互作用的系统，有三个主要目标：1。发现并列举网络系统的基本原理。在没有直接规定的情况下，使用结构、动态和人口统计数据来推断功能交互。预测网络结构和人口统计，并使用数学和计算方法来操纵现有网络和设计具有所需属性的新网络。网络为表示和分析交互实体的复杂系统提供了一个强大的工具。它们出现在物理、生物、社会和信息科学中，可以用来表示蛋白质之间的相互作用、人与人之间的友谊、网页之间的超链接等等。网络由一组实体（称为“顶点”）组成，这些实体通过纽带（称为“边”）相互连接。大多数网络研究考虑具有单一类型边缘的静态网络，并且已经开发了许多工具来研究此类网络。然而，应用程序中出现的网络通常更复杂。它们可能是“动态的”，因为它们可能具有时间依赖性结构，这可能代表委员会分配或政治家投票模式随时间的变化，或者在运动活动的不同部分，大脑区域的不同功能连通性。他们也可以是“多元的”，因为他们包括多种边缘类型，比如通过共同的委员会任务和相似的投票模式联系在一起的政治家。虽然研究人员早就意识到应用中的网络是动态和多路的，但直到最近几年才有高质量的数据可以有效地研究这种情况。我最近帮助开发了一个网络的“多片”框架，以及配套的算法工具，可用于研究时间依赖性和多路网络（Mucha et al, Science, 2010）。多层框架偏离了网络科学的规范，因为它使用三维数字数组而不是通常的邻接矩阵（即二维数组）来制定网络。这篇2010年的论文开发了一种多片网络中的工具，用于算法检测被称为“社区”的结构，每个社区由一组顶点组成，这些顶点之间的连接比网络中其他顶点之间的连接更密集。不同类型的网络边缘的存在，它们是相互关联的，并随着时间的推移而演变，提出了关于网络结构的概念和实际问题，而多片框架可以用来尝试回答这些问题。我们2010年论文中的原理证明为研究生物学和政治学等学科的动态和多元网络铺平了道路。然而，将此框架应用于实践中的应用程序将需要在概念和面向应用程序方面付出相当大的努力。拟议的方案将在实现这一目标方面取得重大进展，特别是在社区结构方面。通过我的合作（见支持信），我可以访问政治学和生物学的大型数据集。克服动态和多路数据的挑战性将在概念和应用方面产生有趣的见解。对于只有单一边缘类型的静态网络中的社区结构，我们了解得很多，但是对于动态或多路网络中的社区结构，我们几乎一无所知。应用程序中遇到的大多数网络都有这样的特性，我的建议直接解决了这个问题。

Network science, the study of systems of interconnected entities and their functional interactions, has three principal goals:1. Discover and enumerate the basic principles of networked systems.2. Use structure, dynamics, and demographics to infer functional interactions when they are not directly prescribed.3. Predict network structure and demographics, and use mathematical and computational methods to manipulate existing networks and design new networks with desired properties.Networks provide a powerful tool for representing and analysing complex systems of interacting entities. They arise in the physical, biological, social, and information sciences and can be used to represent interactions between proteins, friendships between people, hyperlinks between web pages, and so on. A network consists of a set of entities (called "vertices") that are connected to each other by ties (called "edges").Most studies of networks consider static networks with a single type of edge, and numerous tools have been developed to study such networks. However, networks that arise in applications are often more complicated. They can be "dynamic" in that they can have a time-dependent structure, which might represent changes in the committee assignments or voting patterns of politicians over time or different functional connectivity of brain regions during different parts of a motor activity. They can also be "multiplex" in that they include multiple edge types, such politicians who are connected both via common committee assignments and similar voting patterns.Although researchers have long been aware that networks in applications are both dynamic and multiplex, it is only in the past few years that high-quality data has become available to study such situations effectively. I recently helped develop a "multislice" framework for networks, along with accompanying algorithmic tools, which can be used for studying time-dependent and multpliex networks (Mucha et al, Science, 2010). The multislice framework departs from the norm in network science, as it formulates networks using three-dimensional arrays of numbers instead of the usual adjacency matrices (i.e., two-dimensional arrays). The 2010 paper developed a tool in multislice networks for the algorithmic detection of structures known as "communities", each of which consists of a set of vertices that are connected more densely to each other than they are to vertices in the rest of the network. The presence of different types of network edges, which are interrelated and evolve in time, raises conceptual and practical questions about network structure, and the multislice framework can be used to try to answer them. The proof of principle in our 2010 paper paves the way to studying dynamic and multiplex networks in subjects such as biology and political science. However, applying this framework to applications in practice will require considerable effort on both conceptual and application-oriented fronts. The proposed programme will make major headway towards this goal, especially in the area of community structure. Through my collaborations (see Letters of Support), I have access to large data sets from political science and biology. Overcoming the challenging nature of dynamic and multiplex data will yield interesting insights both conceptually and for applications. Much is known about community structure in static networks with only a single type of edge, but almost nothing is understood about community structure in either dynamic or multiplex networks. Most networks encountered in applications have such features, and my proposal directly addresses this issue.