Networks involved in information processing often have their nodes arranged hierarchically, with the majority of connections occurring in adjacent levels. However, despite being an intuitively appealing concept, the hierarchical organization of large networks, such as those in the brain, is difficult to identify, especially in absence of additional information beyond that provided by the connectome. In this paper, we propose a framework to uncover the hierarchical structure of a given network, that identifies the nodes occupying each level as well as the sequential order of the levels. It involves optimizing a metric that we use to quantify the extent of hierarchy present in a network. Applying this measure to various brain networks, ranging from the nervous system of the nematode Caenorhabditis elegans to the human connectome, we unexpectedly find that they exhibit a common network architectural motif intertwining hierarchy and modularity. This suggests that brain networks may have evolved to simultaneously exploit the functional advantages of these two types of organizations, viz., relatively independent modules performing distributed processing in parallel and a hierarchical structure that allows sequential pooling of these multiple processing streams. An intriguing possibility is that this property we report may be common to information processing networks in general.

中文翻译：

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大脑网络的层次结构索引揭示了复杂的纠缠组织结构


参与信息处理的网络通常将其节点分层排列，大多数连接发生在相邻级别。然而，尽管这是一个直观上吸引人的概念，但大型网络（例如大脑中的网络）的层次结构很难识别，特别是在缺乏连接组提供的附加信息的情况下。在本文中，我们提出了一个框架来揭示给定网络的层次结构，该结构识别占据每个级别的节点以及级别的顺序。它涉及优化我们用来量化网络中存在的层次结构范围的指标。将这种方法应用于各种大脑网络，包括线虫的神经系统秀丽隐杆线虫对于人类连接组，我们意外地发现它们表现出一种共同的网络架构主题，即层次结构和模块化交织在一起。这表明大脑网络可能已经进化到同时利用这两种类型组织的功能优势，即并行执行分布式处理的相对独立的模块和允许顺序池化这些多个处理流的分层结构。一个有趣的可能性是，我们报告的这种属性可能对于一般信息处理网络来说是常见的。