Statistical Mechanics of Complex Networks
Statistical Mechanics of Complex Networks
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DOI：
10.1002/9783527627981.ch2
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发表时间：
2009-08
期刊：
影响因子：
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通讯作者：
S. Thurner
中科院分区：
文献类型：
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作者：
S. Thurner
最近在网络理论中令人印象深刻的定量研究的一个解释可能是，它为理解复杂系统提供了一个有前途的工具。网络理论主要关注离散的大规模拓扑结构的统计描述，而不是其元素相互作用的微观细节。这种观点允许人们自然地对待集体现象，这些现象往往是复杂系统的一个组成部分，例如生物或社会经济现象。网络理论的吸引力很大程度上来自于这样一个发现，即许多网络，无论是自然的还是人造的，都表现出某种普遍性，这意味着它们中的大多数属于三类网络之一：随机网络、无标度网络和小世界网络。然而，也许最重要的是，由于网络理论在概念上的直观性，从第一原理出发，我们似乎可以对网络理论有一个完整而连贯的理解，用一组宏观参数来描述网络已经成为标准做法。这些参数通常提供了对网络内链接的统计、聚类程度或某些动机发生的统计的实际理解。有了这些知识，在许多情况下就足以可靠地描述特定网络的结构、鲁棒性和性能或功能。通常，网络不是有目的地设计的结构，而是作为微观规则的结果出现的，这些规则支配着单个节点的链接和重新链接动态。这些规则可以是非常普遍的，涵盖了从纯粹的确定性到完全统计性的巨大变化。科学史上的里程碑之一是发现热力学定律可以与微观理论，即所谓的统计力学相联系，并以之为基础。玻尔兹曼的统计力学是一个框架，它将微观粒子的性质与物质的宏观整体性质联系起来，从而解释热力学。宏观世界和微观世界之间的形式联系是概念
An explanation for the impressive recent quantitative efforts in network theory might be that it provides a promising tool for understanding complex systems. Network theory is mainly focused on statistical descriptions of discrete large-scale topological structures rather than on microscopic details of interactions of its elements. This viewpoint allows one to naturally treat collective phenomena that are often an integral part of complex systems, such as biological or socioeconomic phenomena. Much of the attraction of network theory arises from the discovery that many networks, natural or manmade, exhibit some sort of universality, meaning that most of them belong to one of three classes: random, scale-free, and small-world networks. Maybe most important, however, is that, due to its conceptually intuitive nature, network theory seems to be within realistic reach of a full and coherent understanding from first principles.It has become standard practice to describe networks by a set of macroscopic parameters. These parameters usually provide a practical understanding about the statistics of linking within the network, the degrees of clustering, or the statistics of occurrence of certain motives. With this knowledge it is in many cases sufficient to reliably characterize a particular network in terms of its structure, robustness, and performance or function. Often networks are not structures that are purposefully designed but that emerge as a consequence of microscopic rules that govern the linking and relinking dynamics of individual nodes. These rules can be very general and cover a huge variety, ranging from purely deterministic to fully statistical ones. One of the milestones in the history of science was the discovery that the laws of thermodynamics could be related to–and based on–a microscopic theory, so-called statistical mechanics. The statistical mechanics of Boltzmann is a framework that relates the properties of microscopic particles to the macroscopic bulk properties of matter, thereby explaining thermodynamics. The formal link between the macro-and the microworld is the concept