10.1371/journal.pone.0151027.g005 Evangelos Papalexakis Evangelos Papalexakis Bryan Hooi Bryan Hooi Konstantinos Pelechrinis Konstantinos Pelechrinis Christos Faloutsos Christos Faloutsos Numerical demonstration of Lemma 1. Public Library of Science 2016 network models hop count r node pairs C hop neighborhood network datasets power-law pattern hop-count r scale-free distribution power-law exponent percentile distance power-hop exponent h Pervasive Observation Real Complex Networks Complex networks fractal correlation dimension D 2 scale-free degree distribution 2016-03-14 00:54:17 Figure https://plos.figshare.com/articles/figure/Numerical_demonstration_of_Lemma_1_/3965145 <p>Using a seed network with large enough diameter to obtain statistically meaningful results (top left figure), we validate Lemma 1. As we can see at the top right figure the number of pair of nodes within distance <i>r</i> expected from Lemma 1 is equal to the one computed from the networks. Furthermore, the computed power-hop exponent is very close to the one expected from our lemma as well (bottom left figure). Finally, the actual scaling behavior for the networks after each Kronecker iteration are presented at the bottom right figure.</p>