Quantifying Complexity in Networks: The von Neumann Entropy
Quantifying Complexity in Networks: The von Neumann Entropy
复制标题
DOI：
10.4018/jats.2009071005
复制
发表时间：
2009-10
期刊：
影响因子：
--
通讯作者：
Filippo Passerini;S. Severini
中科院分区：
文献类型：
--
作者：
Filippo Passerini;S. Severini
作者引入了一种新的熵概念，目的是量化网络中的无序/不确定性。这是基于拉普拉斯算子的，它正是某些量子力学状态的冯·诺依曼熵。值得注意的是，冯诺依曼熵依赖于光谱性质，它可以有效地计算。这里描述的分析结果和数值计算导致我们得出结论，冯诺依曼熵增加下的边缘添加，增加与网络的正则性和其连接组件的数量。这个概念打开了量子信息理论和复杂网络在统计水平上的研究之间的广泛接口的前景。
The authors introduce a novel entropic notion with the purpose of quantifying disorder/uncertainty in networks. This is based on the Laplacian and it is exactly the von Neumann entropy of certain quantum mechanical states. It is remarkable that the von Neumann entropy depends on spectral properties and it can be computed efficiently. The analytical results described here and the numerical computations lead us to conclude that the von Neumann entropy increases under edge addition, increases with the regularity properties of the network and with the number of its connected components. The notion opens the perspective of a wide interface between quantum information theory and the study of complex networks at the statistical level.