The Structure and Dynamics of Social Networks and Other Networked Systems

这项资助下的研究将集中在网络结构的数学分析和建模，如社交网络和计算机网络。 三个具体项目构成了将要开展的工作的核心。 第一个将开发用于检测和分析网络中密集子图的计算机算法，也称为模块或社区，除了提供大规模网络结构的窗口外，还可以作为粗粒度技术，可视化，图形布局以及自动网络总结和大型网络数据集中的特征提取的基础。第二个项目将研究网络对网络节点故障的恢复能力，这一专题直接应用于互联网等通信网络以及疾病通过社交网络传播的理论。 该项目将特别关注网络中多个独立路径的存在所产生的弹性以及k分量的相关图论概念。 第三个项目将侧重于开发探索性分析方法，利用机器学习和统计技术，以无监督方式发现大型网络数据集的结构。 这些技术旨在从实验网络数据集中提取新知识，例如大规模社交网络或生物网络。 互联网、万维网、在线社交网络以及为活细胞提供动力的生物网络只是过去几年中占据头条新闻的几个例子。 该基金资助的研究重点是开发基础新数学和实用计算机方法，以理解和分析科学家可用的丰富网络数据。 我们目前对网络的理解存在一个重大问题，这是由我们所面临的许多网络的庞大规模造成的。 例如，网络上的节点数量高达数十亿，而利用现有资源，完全可视化整个网络是不可能的（即使可能，也可能不是很有用）。 这里要开发的技术专注于回答网络“看起来像什么”的问题，即使我们不能直接看到它。 其中一个项目将侧重于网络中的“模块”-一组紧密连接的节点，它们可能对应于社会网络中的集团或社区，或生物网络中的功能模块-并将开发自动发现这些模块的计算机方法，使实验者能够揭示网络的大规模结构。 另一个项目将研究网络对节点故障的恢复能力，这一问题对于维持通信网络的运作至关重要，也关系到制定有效的疫苗接种战略，以防止疾病在社交网络上传播。 第三个项目将开发自动化方法，以揭示节点之间连接模式中迄今未见的缺陷，使科学家能够从网络数据中提取有用的信息，即使是在我们目前的理解非常不完整的新兴领域。

The research funded under this grant will focus on the mathematical analysis and modeling of the structure of networks such as social networks and computer networks. Three specific projects form the core of the work to be undertaken. The first will develop computer algorithms for the detection and analysis of dense subgraphs within networks, also called modules or communities, which, in addition to providing a window on large-scale network structure, can serve as a foundation for coarse-graining techniques, visualization, graph layout, and automated network summarization and feature extraction in large network data sets. The second project will look at the resilience of networks to the failure of network nodes, a topic that has direct applications in communications networks such as the Internet as well as in the theory of the spread of disease through social networks. The project will look in particular at the resilience created by the existence of multiple independent paths in networks and the related graph theoretical concept of k-components. The third project will focus on the development of exploratory analysis methods for discovering structure in large network data sets in an unsupervised fashion, making use of machine learning and statistical techniques. These techniques are aimed at the extraction of new knowledge from experimental network data sets such as large-scale social networks or biological networks.Networks occur widely in the sciences and technology. The Internet, the World Wide Web, online social networks, and the biological networks that power living cells are just a few of the examples that have grabbed headlines in the last few years. The research funded under this grant focuses on the development of both fundamental new mathematics and practical computer methods for understanding and analyzing the wealth of network data that is becoming available to scientists. A significant problem with our current understanding of networks is created by the sheer size of many of the networks we are faced with. The web, for example, has nodes numbering in the billions, and a complete visualization of the entire network is impossible with current resources (and probably wouldn't be very useful even if it were possible). The techniques to be developed here focus on answering the question of what a network "looks like," even when we can't look at it directly. One project will focus on "modules" in networks -- groups of tightly connected nodes, which may correspond to cliques or communities in a social network or functional modules in a biological network -- and will develop computer methods for automatically discovering these modules, allowing the experimenter to uncover the large-scale structure of a network. Another project will look at resilience of networks to the failure of their nodes, an issue that is of prime importance for the maintenance of functioning communication networks and is also related to the development of efficient vaccination strategies to prevent the spread of disease over social networks. A third project will develop automated methods for revealing hitherto unseen regularities in the connection patterns between nodes, allowing scientists to extract useful information from network data even in emerging areas where our current understanding is very incomplete.