Correlation between Dimensions based on Neighbors in Multidimensional Networks and a Method for Adding an Edge to Strengthen or Weaken the Correlation

In recent years, various systems have become more complex, and the network structures used to model them have also become more complex. The concept of multidimensional network has been proposed in complex networks and multidimensional networks are modeled as graphs. The properties of multidimensional networks have been studied focusing on factors such as degree, neighbors, eccentricity, closeness and betweenness. In this paper, we define the correlation coefficient between dimensions based on neighbors in a multidimensional network, and discuss the change in correlation between dimensions based on neighbors due to addition of an edge in multidimensional networks and a method for adding an edge to strengthen or weaken the correlation.