Symmetry in Complex Networks
Symmetry in Complex Networks
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DOI：
10.3390/sym3010001
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发表时间：
2011-01
期刊：
影响因子：
--
通讯作者：
A. Garrido
中科院分区：
文献类型：
--
作者：
A. Garrido
在本文中，我们分析了几个与图相关的概念，如它们的度、熵或它们的对称/不对称程度。这些概念在不同类型的系统的研究中被证明是有用的，特别是在复杂网络的分析中。系统可以被定义为作为一个整体一起运行的任何组件集。系统的观点使我们能够孤立世界的一部分，因此，我们可以专注于那些比其他方面更紧密地互动的方面。网络科学从物理、工程、生物、语义等不同领域分析不同网络之间的互联。目前基于图论的复杂网络定量分析的发展已经迅速转化为对脑网络组织的研究。大脑的系统具有复杂的网络特征--例如小世界的拓扑结构、高度连接的中枢和模块化。这些网络不是随机的。许多不同网络的拓扑结构表现出惊人的相似性，如无标度结构，度分布服从幂定律。非常不同的系统怎么会有相同的底层拓扑特征？对这些网络进行建模和刻画，寻找它们的支配规律，是目前的研究方向。因此，我们将专门介绍复杂网络中的对称性度量，并强调它们与信息度量和信息熵之间的密切关系。
In this paper, we analyze a few interrelated concepts about graphs, such as their degree, entropy, or their symmetry/asymmetry levels. These concepts prove useful in the study of different types of Systems, and particularly, in the analysis of Complex Networks. A System can be defined as any set of components functioning together as a whole. A systemic point of view allows us to isolate a part of the world, and so, we can focus on those aspects that interact more closely than others. Network Science analyzes the interconnections among diverse networks from different domains: physics, engineering, biology, semantics, and so on. Current developments in the quantitative analysis of Complex Networks, based on graph theory, have been rapidly translated to studies of brain network organization. The brain's systems have complex network features—such as the small-world topology, highly connected hubs and modularity. These networks are not random. The topology of many different networks shows striking similarities, such as the scale-free structure, with the degree distribution following a Power Law. How can very different systems have the same underlying topological features? Modeling and characterizing these networks, looking for their governing laws, are the current lines of research. So, we will dedicate this Special Issue paper to show measures of symmetry in Complex Networks, and highlight their close relation with measures of information and entropy.