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>