Signless-laplacian eigenvector centrality: A novel vital nodes identification method for complex networks

•An iterative centrality updated framework between vertices and edges is proposed.•This iterative framework is convergent.•The convergence values of vertices are defined as the new vertex centralities.•The new centrality scores correspond to the principal eigenvalues of the signless-Laplacian matrix.•When applying on many data sets from various fields, all obtain reliable and even better results. 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.