摘要翻译：
在对大型网络和小型网络的研究中，通常进行简单的随机游动，即随机游动者以均匀的概率从一个节点跳到它的相邻节点。这种随机游动的性质与网络的组合性质密切相关。在本文中，我们提出用Ruelle-Bowens随机游动代替，其概率转移的选择是为了最大化游动在未加权图上的熵率。如果对图进行加权，则优化自由能而不是熵率。具体来说，我们引入了大型网络的中心性测度，即Ruelle-Bowens随机游动得到的平稳分布；我们把它命名为熵秩。我们引入了一个更一般的版本，能够处理断开网络，在自由能秩的名称下。我们比较了这些中心度度量与经典的PageRank和HITS在玩具和现实生活中的性质，特别是它们对网络的小修改的鲁棒性。我们的中心度度量比PageRank有更好的鉴别能力，能够清楚地区分PageRank所保存的几乎同样有趣的页面，并且对图的中等尺度细节更敏感。
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英文标题：
《Centrality measures and thermodynamic formalism for complex networks》
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作者：
Jean-Charles Delvenne and Anne-Sophie Libert
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最新提交年份：
2010
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分类信息：

一级分类：Physics        物理学
二级分类：Data Analysis, Statistics and Probability        数据分析、统计与概率
分类描述：Methods, software and hardware for physics data analysis: data processing and storage; measurement methodology; statistical and mathematical aspects such as parametrization and uncertainties.
物理数据分析的方法、软硬件：数据处理与存储；测量方法；统计和数学方面，如参数化和不确定性。
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一级分类：Physics        物理学
二级分类：Statistical Mechanics        统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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一级分类：Physics        物理学
二级分类：Physics and Society        物理学与社会
分类描述：Structure, dynamics and collective behavior of societies and groups (human or otherwise). Quantitative analysis of social networks and other complex networks. Physics and engineering of infrastructure and systems of broad societal impact (e.g., energy grids, transportation networks).
社会和团体（人类或其他）的结构、动态和集体行为。社会网络和其他复杂网络的定量分析。具有广泛社会影响的基础设施和系统（如能源网、运输网络）的物理和工程。
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英文摘要：
  In the study of small and large networks it is customary to perform a simple random walk, where the random walker jumps from one node to one of its neighbours with uniform probability. The properties of this random walk are intimately related to the combinatorial properties of the network. In this paper we propose to use the Ruelle-Bowens random walk instead, whose probability transitions are chosen in order to maximise the entropy rate of the walk on an unweighted graph. If the graph is weighted, then a free energy is optimised instead of entropy rate.   Specifically, we introduce a centrality measure for large networks, which is the stationary distribution attained by the the Ruelle-Bowens random walk; we name it Entropy Rank. We introduce a more general version, able to deal with disconnected networks, under the name of Free Energy Rank. We compare the properties of those centrality measures with the classic PageRank and HITS on both toy and real-life examples, in particular their robustness to small modifications of the network. It is observed that our centrality measures have a better discriminating power than PageRank, being able to distinguish clearly pages that PageRank holds for almost equally interesting, and is more sensitive to the medium-scale details of the graph.
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PDF链接：
https://arxiv.org/pdf/710.3972