School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, China.
School of Mathematics and Statistics, Henan University, Kaifeng 475004, China.
Sci Rep. 2017 Jan 24;7:41321. doi: 10.1038/srep41321.
Designing node influence ranking algorithms can provide insights into network dynamics, functions and structures. Increasingly evidences reveal that node's spreading ability largely depends on its neighbours. We introduce an iterative neighbourinformation gathering (Ing) process with three parameters, including a transformation matrix, a priori information and an iteration time. The Ing process iteratively combines priori information from neighbours via the transformation matrix, and iteratively assigns an Ing score to each node to evaluate its influence. The algorithm appropriates for any types of networks, and includes some traditional centralities as special cases, such as degree, semi-local, LeaderRank. The Ing process converges in strongly connected networks with speed relying on the first two largest eigenvalues of the transformation matrix. Interestingly, the eigenvector centrality corresponds to a limit case of the algorithm. By comparing with eight renowned centralities, simulations of susceptible-infected-removed (SIR) model on real-world networks reveal that the Ing can offer more exact rankings, even without a priori information. We also observe that an optimal iteration time is always in existence to realize best characterizing of node influence. The proposed algorithms bridge the gaps among some existing measures, and may have potential applications in infectious disease control, designing of optimal information spreading strategies.
设计节点影响排名算法可以深入了解网络的动态、功能和结构。越来越多的证据表明，节点的传播能力在很大程度上取决于其邻居。我们引入了一种具有三个参数的迭代邻居信息收集（Ing）过程，包括变换矩阵、先验信息和迭代次数。Ing 过程通过变换矩阵迭代地从邻居那里收集先验信息，并迭代地为每个节点分配一个 Ing 分数来评估其影响力。该算法适用于任何类型的网络，并包括一些传统的中心度作为特例，如度、半局部、LeaderRank。在强连通网络中，Ing 过程收敛速度取决于变换矩阵的前两个最大特征值。有趣的是，特征向量中心度对应于算法的一个极限情况。通过与八种著名的中心度进行比较，对真实网络上的易感染-感染-清除（SIR）模型的模拟表明，Ing 可以提供更准确的排名，即使没有先验信息。我们还观察到，总是存在一个最佳的迭代次数来实现对节点影响的最佳描述。所提出的算法弥合了一些现有度量之间的差距，并可能在传染病控制、最佳信息传播策略的设计等方面具有潜在应用。
