Network theory is a useful framework for studying interconnected systems of interacting entities. Many networked systems evolve continuously in time, but most existing methods for the analysis of time-dependent networks rely on discrete or discretized time. In this paper, we propose an approach for studying networks that evolve in continuous time by distinguishing between interactions , which we model as discrete contacts, and ties , which encode the strengths of relationships over time. To illustrate our tie-decay network formalism, we adapt the well-known PageRank centrality score to our tie-decay framework in a mathematically tractable and computationally efficient way. We apply this framework to a synthetic example and then use it to study a network of retweets during the 2012 National Health Service controversy in the United Kingdom. Our work also provides guidance for similar generalizations of other tools from network theory to continuous-time networks with tie decay, including for applications to streaming data.

中文翻译：

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连续时间中的衰减网络和基于特征向量的中心性

网络理论是研究相互作用实体的互连系统的有用框架。许多网络系统随时间不断演变，但大多数现有的时间相关网络分析方法依赖于离散或离散时间。在本文中，我们提出了一种方法来研究连续时间演化的网络，通过区分互动 ，我们将其建模为离散接触，以及 关系 ，随着时间的推移对关系的强度进行编码。为了说明我们的 tie-decay 网络形式主义，我们以一种数学上易于处理且计算效率高的方式将众所周知的 PageRank 中心性分数应用于我们的 tie-decay 框架。我们将此框架应用于合成示例，然后使用它来研究 2012 年英国国民健康服务争议期间的转推网络。我们的工作还为其他工具的类似概括提供了指导，从网络理论到具有联系衰减的连续时间网络，包括对流数据的应用。