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.