Corner Centrality of Nodes in Multilayer Networks: A Case Study in the Network Analysis of Keywords

Abstract

In this paper, we present a new method to measure the nodes’ centrality in a multilayer network. The multilayer network represents nodes with different relations between them. The nodes have an initial relevance or importance value. Then, the node’s centrality is obtained according to this relevance along with its relationship to other nodes. Many methods have been proposed to obtain the node’s centrality by analyzing the network as a whole. In this paper, we present a new method to obtain the centrality in which, in the first stage, every layer would be able to define the importance of every node in the multilayer network. In the next stage, we would integrate the importance given by each layer to each node. As a result, the node that is perceived with a high level of importance for all of its layers, and the neighborhood with the highest importance, obtains the highest centrality score. This score has been named the corner centrality. As an example of how the new measure works, suppose we have a multilayer network with different layers, one per research area, and the nodes are authors belonging to an area. The initial importance of the nodes (authors) could be their h-index. A paper published by different authors generates a link between them in the network. The authors can be in the same research area (layer) or different areas (different layers). Suppose we want to obtain the centrality measure of the authors (nodes) in a concrete area (target layer). In the first stage, every layer (area) receives the importance of every node in the target layer. Additionally, in the second stage, the relative importance given for every layer to every node is integrated with the importance of every node in its neighborhood in the target layer. This process can be repeated with every layer in the multilayer network. The method proposed has been tested with different configurations of multilayer networks, with excellent results. Moreover, the proposed algorithm is very efficient regarding computational time and memory requirements.

Keywords

• networks centrality
• multilayer networks
• PageRank centrality
• corner centrality
• author’s keywords