ESD Working Paper Series ESD-WP-2010-01
ESD Working Paper Series ESD-WP-2010-01
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发表时间：
2010
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通讯作者：
Jianxi Luo;C. Magee
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作者：
Jianxi Luo;C. Magee
层级结构广泛存在于进化中的自组织生态、生物、技术和社会网络中，但检测和比较层级结构是困难的。在这里，我们提出了一种度量和技术来定量评估自组织有向网络表现出流层次的程度。流层次结构是网络中一种常见但在理论上被忽视的层次结构形式。我们表明，生态、神经生物学、经济和信息处理网络通常比它们的可比随机网络更具层次性。我们进一步发现，在Linux内核的演化过程中，层次度一直在增加，这证实了Herbert Simon关于在演化过程中出现层次化的早期假设。综上所述，我们的结果表明，层级是现实世界演化网络的核心组织特征，而层级的测量开启了理解自组织网络的结构机制和演化模式的途径。我们的测量技术使得客观地比较不同网络的层次结构和单个网络的不同演化阶段，以及比较不同网络的演化模式成为可能。它可以应用于各种复杂系统，可以表示为有向网络。
Hierarchies occur widely in evolving self-organizing ecological, biological, technological and social networks, but detecting and comparing hierarchies is difficult. Here we present a metric and technique to quantitatively assess the extent to which self-organizing directed networks exhibit a flow hierarchy. Flow hierarchy is a commonly observed but theoretically overlooked form of hierarchy in networks. We show that the ecological, neurobiological, economic and information processing networks are generally more hierarchical than their comparable random networks. We further discovered that hierarchy degree has increased over the course of the evolution of Linux kernels, confirming an early hypothesis by Herbert Simon on the emergence of hierarchy in evolutionary processes. Taken together, our results suggest that hierarchy is a central organizing feature of real-world evolving networks, and the measurement of hierarchy opens the way to understand the structural regimes and evolutionary patterns of self-organizing networks. Our measurement technique makes it possible to objectively compare hierarchies of different networks and of different evolutionary stages of a single network, and compare evolving patterns of different networks. It can be applied to various complex systems, which can be represented as directed networks.