论文标题
通过连续时间量子步行在定向网络中排名节点
Ranking nodes in directed networks via continuous-time quantum walks
论文作者
论文摘要
根据$ n $尺寸（$ n $是节点的数量），基于统一的，连续的时间量子步行（CTQW）的定向网络的四个新的中心度措施进行了介绍，测试和讨论。这些方法背后的主要思想在于重新估算经典的热门单曲和Pagerank算法作为对称矩阵的特征向量问题，并将这些对称矩阵用作CTQWS的汉密尔顿人，以获取单位进化操作员。初始状态的选择也至关重要。测试了两种选择：具有统一职业的向量和矢量加权的W.R.T.两种方法是基于衍生的汉密尔顿人，两种方法使用了帕格兰克衍生的哈密顿式化学。节点的中心分数定义为平均职业值。所有方法均已在一组小的简单图表上进行了测试，以发现可能的明显缺点，然后在大量的人工生成的大型图中进行了比较，以便与经典的命中和Pagerank进行比较。数值结果表明，尽管在分析小图时在三种方法中发现了一些病理，但所有方法在较大图中的第一个和前十个节点均有效。我们评论结果，并提供一些对古典方法和量子方法之间良好性的见解。
Four new centrality measures for directed networks based on unitary, continuous-time quantum walks (CTQW) in $n$ dimensions -- where $n$ is the number of nodes -- are presented, tested and discussed. The main idea behind these methods consists in re-casting the classical HITS and PageRank algorithms as eigenvector problems for symmetric matrices, and using these symmetric matrices as Hamiltonians for CTQWs, in order to obtain a unitary evolution operator. The choice of the initial state is also crucial. Two options were tested: a vector with uniform occupation and a vector weighted w.r.t.~in- or out-degrees (for authority and hub centrality, respectively). Two methods are based on a HITS-derived Hamiltonian, and two use a PageRank-derived Hamiltonian. Centrality scores for the nodes are defined as the average occupation values. All the methods have been tested on a set of small, simple graphs in order to spot possible evident drawbacks, and then on a larger number of artificially generated larger-sized graphs, in order to draw a comparison with classical HITS and PageRank. Numerical results show that, despite some pathologies found in three of the methods when analyzing small graphs, all the methods are effective in finding the first and top ten nodes in larger graphs. We comment on the results and offer some insight into the good accordance between classical and quantum approaches.
