σ-Space for real-world networks: A correlation analysis of decay centrality vs. degree centrality and closeness centrality

We analyze a suite of 48 real-world networks and compute the decay centrality (DEC) of the vertices for the complete range of values for the decay parameter d e (0, 1) as well as determine the Pearson’s correlation coefficient (PCC) between the DECd values and degree centrality (DEG) and closeness centrality (CLC). We observe PCC(DECσ, DEG) to decrease with increase in d and PCC(DECd, CLC) to decrease with decrease in d. We define the σ-spacer for a real-world network with respect to the DEG, DEC, CLC correlation as the difference between the maximum and minimum d values under which we observe a particular level of correlation (r) between the DEC, DEG and DEC, CLC metrics respectively. We show that the PCC(DEG, CLC) values for the real-world networks exhibit a very strongly positive correlation with the dspacer values and demonstrate that one could predict the σ-spacer value for a real-world network using the PCC(DEG, CLC) value for that network. We also analyze the impact of various topological measures on the σ-spacer values for the real-world networks.