论文标题
复杂网络吉布斯状态的渐近熵
Asymptotic entropy of the Gibbs state of complex networks
论文作者
论文摘要
在这项工作中，我们研究了与图相对应的吉布斯状态的熵。 Gibbs状态是从与图形相关的Laplacian，归一化的Laplacian或邻接矩阵获得的。我们计算了几类图形的吉布斯状态的熵，并通过更改图顺序和温度研究了它们的行为。我们使用ERDőS-Rényi，Watts-Strogatz，Barabási-Albert和Chung-Lu图模型以及一些真实世界图的数值模拟来说明我们的分析结果。我们的结果表明，与随机的Erdős-rényi图相比，Gibbs熵随温度的函数的函数不同。
In this work we study the entropy of the Gibbs state corresponding to a graph. The Gibbs state is obtained from the Laplacian, normalized Laplacian or adjacency matrices associated with a graph. We calculated the entropy of the Gibbs state for a few classes of graphs and studied their behavior with changing graph order and temperature. We illustrate our analytical results with numerical simulations for Erdős-Rényi, Watts-Strogatz, Barabási-Albert and Chung-Lu graph models and a few real-world graphs. Our results show that the behavior of Gibbs entropy as a function of the temperature differs for a choice of real networks when compared to the random Erdős-Rényi graphs.
