Node Dissimilarity Index for Complex Network Analysis

Abstract: We propose a principal component analysis (PCA)-based approach to quantify (the node dissimilarity index, NDI) the extent of dissimilarity among nodes in a network with respect to values incurred for a suite of node-level metrics (like centrality metrics). We subject the dataset (n nodes and their values incurred for four commonly studied centrality metrics: degree, eigenvector, betweenness and closeness) to PCA and retain the m ( <= 4) principal components (with variance >= 1.0). We construct an n-node dissimilarity matrix whose entries are the absolute difference (if m = 1) or Euclidean distance (if M > 1) of the principal component coordinates of the corresponding nodes. We compute NDI (>= 1.0) to be the ratio of the principal Eigenvalue of the node dissimilarity matrix and average of entries in the node dissimilarity matrix. The larger the NDI, the greater the dissimilarity among the node-level metrics (centrality metrics) values considered for analysis.