# Corner Centrality of Nodes in Multilayer Networks: A Case Study in the Network Analysis of Keywords
## 1 Introduction
### Main Contribution  
This paper proposes a new node centrality measure in a multilayer network. This new centrality measure has been called the \"Corner centrality\", (the name was inspired by the [PERSON] corner detector for images [25]). The corner centrality algorithm assigns a high centrality value to a node in the target layer when all reference layers recognize that node as a node with a high relative importance value. We say that a node in the target layer has a high relative importance from the point of view of a reference layer, when the node has an initial value of importance that stands out over the importance of the nodes of its neighborhood in that reference layer. For example, if we are looking for diplomats to be the negotiators between countries in conflict, these diplomats must be positively recognized by all the countries in conflict. If only one of them does not like that diplomatic person, deals cannot occur. The initial importance value of each node is an implicit characteristic of the node. For example, in a multilayer network where the relationships between authors who publish in certain scientific journals are represented. In turn, scientific journals are related if they are in the same area of research. The initial level of importance for each author could be their h-index. Additionally, the initial level of importance for each journal could be its impact factor. In the event that this initial information of importance is unknown, an alternative is to take the degree of the node as the initial value of importance. The corner centrality measure can be applied to networks with intralinks and/or interlinks, and the algorithm is independent from the multilayer network structure. Additionally, the corner centrality measure can be used with disconnected graphs. Section 3.1.2 will provide an example where we will apply the method on a multilayer network with layers containing disconnected graphs. The only restriction is that two nodes in different layers connected (by an interlink) must have an initial value of importance, and the importance must contain information from the same source. In particular, we suppose that a set of researchers are related because they are authors of the same paper, and the researchers are grouped per research area, defining a layer. However, the paper's authors can be in different areas, and in that case, interlinks would represent their relations. Moreover, the initial importance of these nodes can be, for example, the h-index value of the researchers. When the multilayer network is a multiplex network, both the initial value of importance of the nodes as well as the relationships between them can be different. To test the performance of the corner centrality measure, we performed three experiments. In the first and second experiments, we used multiplex networks. The results were compared with the APABI method [13] and Pagerank versatility method [26]. The APABI method is characterized as an Adapted Pagerank measure that incorporates the informational features of the nodes as the measure of the initial importance. Since the APABI method can only be used on multiplex networks, in the first experiment, we replicated a multiplex network defined in [13] to test our centrality measure. Additionally, the method was compared to the Pagerank versatility method in this first experiment. The Pagerank versatility method expanded on the idea of Google's Pagerank centrality [27] for multilayer networks with interlinks. In this case, we used the Florentine Family multilayer network to compare Pagerank versatility and corner centrality. To apply the corner centrality to a Florentine Family multilayer network, we took the initial value of importance as the degree of the node. The second experiment aimed to deduce the most relevant author keywords in the area of computer science. To this aim, we used the information from Scopus and Google Trend to define the initial importance of the nodes.