# Corner Centrality of Nodes in Multilayer Networks: A Case Study in the Network Analysis of Keywords
## 1 Introduction
Furthermore, this model was modified to obtain a measure of the centrality of the nodes in a biplex network [13]. In social networks, datasets need a description to support different relationships between different types of entities, namely, a system with information from researchers, articles, and institutions [14]. In biology, the different interactions in a system can be modeled as a multilayer network, such as interactions between genes and proteins, genes and diseases, or diseases and drugs [15]. Multilayer networks have also made it possible to represent and study intercellular communications in tissues. For example, a disruption in intercellular communications can trigger diseases [8]. In these examples, every type of entity is grouped into a layer. We can distinguish two types of multilayer networks: multiplex networks and networks with interconnected layers [16]. In multiplex networks, layers have the same set of vertices, and interlayer edges are defined between the same vertices at different layers. A particular case of this is when the network has the same links in each layer, and the only difference is the importance of the entity in each layer. A type of multiplex network is a _temporal multilayer network_ in which each node is connected to itself over discrete layers that represent time periods (for example, a multilayer network describing the temporal evolution of Facebook). In contrast, in interconnected networks, the interlayer edges would connect between different entities (for example, documents and researchers). In Figure 1, MLN1 and MLN2 are multiplex networks, and MLN3 and MLN4 are interconnected networks. Studies of multilayer networks show the importance of obtaining the centrality nodes [17; 18; 19]. The centrality of a node is defined as a ranking among the nodes of a multilayer network. For example, with this information, a user can establish the influencers in a social network, the most effective drugs for different genetic problems, or even the airport where a large number of aerial enterprises are taking off. Computing central nodes is also very important when designing routes in wireless sensor networks (WSNs) in order to reduce delays and energy consumption, as well as improving the routing overlap [19; 20]. Central nodes are also important when determining the size of a network for different fields, such as computer science, social networks, or mathematical modeling, among others [21]. There are different techniques that can be used to obtain the centrality of a node in multiplex networks without interlinks. Multiplex Pagerank [22] calculates the centrality of a node across the different layers. Other algorithms, such as Multiplex Eigenvector Centralities [17] and Functional Multiplex PageRank [18], associate a different influence with the links of different layers that weigh their contribution to the centrality of the nodes. Additionally, classical centrality measures have been redefined to be applied to multiplex networks. Thus, in [23] they redefined the betweenness centrality measure to apply to a multiplex network. In general multilayer networks, the algorithms based on versatility and communicability can be applied to obtain the centrality of a node [24].