Identifying important and influential nodes in complex networks is crucial in understanding, controlling, accelerating or terminating spreading processes for information, diseases, innovations, behaviors, and so on. Many existing centrality methods evaluate a node’s importance (or centrality) according to its neighbors, but the effects of its incident edges are always ignored or treated equally. However, in reality, edges always play different roles, which are usually measured by the edge centrality. Note that the centrality of a vertex is affected by the centralities of its incident edges, and conversely the centrality of an edge is determined by the centralities of its two endpoints. In this paper, we present a novel way to evaluate the centrality for both nodes and edges simultaneously by constructing a mutually updated iterative framework. Furthermore, we will prove that the node centralities obtained by this framework are actually the principal eigenvector of the signless-laplacian matrix of the input network, thus we call this new node centrality method as signless-laplacian eigenvector centrality method. We test it on several classical data sets and all produce satisfying results. It is expected to have a promising applications in the future.

识别复杂网络中的重要和有影响力的节点对于理解，控制，加速或终止信息，疾病，创新，行为等的传播过程至关重要。许多现有的中心度方法根据节点的邻居来评估节点的重要性（或中心性），但始终忽略或平等对待其入射边缘的影响。但是，实际上，边缘始终扮演着不同的角色，这通常由边缘中心性来衡量。请注意，顶点的中心点受其入射边缘的中心点影响，相反，边缘的中心点由其两个端点的中心点确定。在本文中，我们提出了一种新颖的方法，即通过构造一个相互更新的迭代框架来同时评估节点和边缘的中心性。此外，我们将证明通过该框架获得的节点中心性实际上是输入网络的无符号-拉普拉斯矩阵的主要特征向量，因此我们将这种新的节点中心性方法称为无符号-拉普拉斯特征向量中心性方法。我们在几个经典数据集上对其进行了测试，并且都产生了令人满意的结果。有望在将来有广阔的应用前景。