使用Infomap映射内存和多层网络中的高阶网络流
Mapping higher-order network flows in memory and multilayer networks with Infomap
摘要：
通过简化和突出重要的动态模式来理解复杂系统，需要对高阶网络流进行建模和映射。然而，复杂的系统有多种形式，需要一系列的表示，包括内存和多层网络，这反过来又要求通用的社区检测算法，以揭示重要的模块化流程。在这里，我们表明，各种形式的高阶网络流可以表示在一个统一的方式与网络，区分物理节点表示一个~复杂的系统的对象从状态节点描述对象之间的流。此外，这些所谓的稀疏记忆网络允许被称为映射方程的信息理论社区发现方法从一系列不同的高阶交互（例如多步骤、多源和时间数据）中识别数据中的重叠和嵌套的流模块。本文推导了稀疏存储网络的映射方程，并描述了它的搜索算法Infomap，它可以充分利用稀疏存储网络的灵活性。它们一起提供了一个通用的解决方案，以揭示通过复杂系统的高阶流中的重叠模块模式。
英文摘要：
Comprehending complex systems by simplifying and highlighting important dynamical patterns requires modeling and mapping higher-order network flows. However, complex systems come in many forms and demand a range of representations, including memory and multilayer networks, which in turn call for versatile community-detection algorithms to reveal important modular regularities in the flows. Here we show that various forms of higher-order network flows can be represented in a unified way with networks that distinguish physical nodes for representing a~complex system's objects from state nodes for describing flows between the objects. Moreover, these so-called sparse memory networks allow the information-theoretic community detection method known as the map equation to identify overlapping and nested flow modules in data from a range of~different higher-order interactions such as multistep, multi-source, and temporal data. We derive the map equation applied to sparse memory networks and describe its search algorithm Infomap, which can exploit the flexibility of sparse memory networks. Together they provide a general solution to reveal overlapping modular patterns in higher-order flows through complex systems.
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