复杂网络的中心性测度与热力学形式
Centrality measures and thermodynamic formalism for complex networks
摘要：
在研究小型和大型网络时，通常执行简单的随机行走，其中随机行走者以均匀的概率从一个节点跳到其相邻节点之一。这种随机游走的性质与网络的组合性质密切相关。在本文中，我们建议使用Ruelle-Bowens随机游走，其概率转移的选择，以最大限度地提高熵率的步行在一个未加权的图形。如果图被加权，则自由能被优化而不是熵率。具体来说，我们引入了一个大型网络的中心性度量，这是通过Ruelle-Bowens随机游走获得的平稳分布;我们称之为熵秩。我们介绍一个更通用的版本，能够处理断开的网络，在自由能排名的名称。我们比较了这些中心性措施的性质与经典的PageRank和HITS的玩具和现实生活中的例子，特别是他们的鲁棒性网络的小修改。据观察，我们的中心性措施有一个更好的区分能力比PageRank，能够清楚地区分页面，PageRank持有几乎同样有趣的，是更敏感的中等规模的细节图。
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
