NetSE: Medium: Modeling and Analysis of Network Dynamics

在过去的20年里，数字网络的数量和类型迅速增加，当然是从互联网、其组成的网络和万维网开始。我们现在有各种各样的在线社交网络(OSN)，如Facebook、Twitter、移动自组织网络(MANET)和延迟容忍网络(DTN)。这些网络渗透到我们生活的方方面面，并在商业、商业、通信和连接方面提供越来越广泛的服务。这些网络中的许多网络持续地处于流量的动态状态和/或非常大。例如，MANET或DTN的拓扑结构在不断变化，而Facebook等OSN的拓扑结构也在快速增长和发展。由于此类网络的动态性和规模，其建模、分析和测量具有挑战性。因此，传统的数学方法已经不再适用，需要从根本上采用新的方法。首先是开发有用而准确的模型，捕捉当今的动态--S的社交和科技网络。二是开发和研究一类描述和搜索此类网络的技术。这些技术基于一个非常简单的机制，即让代理通过随机选择去哪里来探索网络。这在数学文献中被称为随机游走，并且已经被证明在静态网络中表现出理想的搜索和表征性质，这在动态网络中显示出希望。最后，许多静态网络表现出所谓的幂定律，即节点邻居数目的分布大致衰减为k&a，其中k是邻居数目，a是大于1的正常数。第三个问题是理解动态网络中的幂定律是什么，这个幂定律是如何形成的，以及它可能对网络的健康产生什么影响。这项工作将对社会产生积极影响，为管理和监测诸如MANET和OSN等数字网络提供更深入的理解和一套工具。该项目包括一项全面的传播计划，其中包括公开发布网络表征工具。该教育计划包括跨专业研讨会，本科生通过REU网站参与研究，以及向南美进行国际推广。

There has been a rapid increase in the number and types of digital networks over the last 2 decades beginning, of course with the Internet, its constituent networks, and the World Wide Web. We now have a wide range of on-line social networks (OSNs) such as Facebook, Twitter, mobile ad hoc networks (MANETs) and delay tolerant networks (DTNs). These networks pervade all aspects of our lives and provide a growing range of services in commerce, business, communications, and connectivity. Many of these networks are continually in a dynamic state of flux and/or extremely large. For example, the topology of a MANET or a DTN is constantly changing, and that of an OSN such as Facebook is rapidly growing and evolving. The modeling, analysis, and measurement of such networks are challenging, due to their dynamism and sizes. As a consequence, traditional mathematical techniques are not suitable and fundamentally new techniques are needed.This research will focus on three interrelated problems. The first is to develop useful and accurate models that capture the dynamics of today?s social and technological networks. The second is to develop and study a class of techniques for characterizing and searching such networks. These techniques are based on a very simple mechanism, namely to let an agent explore the network by randomly choosing where to go. This is known as a random walk in the mathematics literature and has been shown to exhibit desirable search and characterization properties in static networks that shows promise in dynamic networks. Last, many static networks exhibit what is known as a power law, namely that the distribution for the number of neighbors of a node roughly decays as k−a where k is the number of neighbors and a is a positive constant greater than one. The third problem is to understand what constitutes a power law in a dynamic network, how this power law comes to be, and what implications there might be regarding the health of the network.Broader Impact. The work will positively impact society by providing a deeper understanding of and a set of tools for managing and monitoring digital networks such as MANETs and OSNs. The project includes a comprehensive dissemination plan including public release of tools for network characterization. The education plan includes cross-specialty seminars, undergraduate involvement in research through a REU site, and international outreach to South America.