δ-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 δ ∊ (0, 1) as well as determine the Pearson's correlation coefficient (PCC) between the DECδ values and degree centrality (DEG) and closeness centrality (CLC). We observe PCC(DECδ, DEG) to decrease with increase in δ and PCC(DECδ, CLC) to decrease with decrease in δ. We define the δ-spacer for a real-world network with respect to the DEG, DEC, CLC correlation as the difference between the maximum and minimum δ 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 δ-spacer values and demonstrate that one could predict the δ-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 δ-spacer values for the real-world networks.