2017/10/30 by Siddharth Pal, Pal, Siddharth, Armand M. Makowski +1
Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Markov Chains and Monte Carlo Methods #Physics and Society (physics.soc-ph) #Probability (math.PR) #Social and Information Networks (cs.SI) #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.1710.11064
openalex publication_date 2017/10/30 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28
In random graph models, the degree distribution of an individual node should\nbe distinguished from the (empirical) degree distribution of the graph that\nrecords the fractions of nodes with given degree. We introduce a general\nframework to explore when these two degree distributions coincide\nasymptotically in large homogeneous random networks. The discussion is carried\nunder three basic statistical assumptions on the degree sequences: (i) a weak\nform of distributional homogeneity; (ii) the existence of an asymptotic (nodal)\ndegree distribution; and (iii) a weak form of asymptotic uncorrelatedness. We\nshow that this asymptotic equality may fail in homogeneous random networks for\nwhich (i) and (ii) hold but (iii) does not. The counterexample is found in the\nclass of random threshold graphs. An implication of this finding is that random\nthreshold graphs cannot be used as a substitute to the Barab 'asi-Albert model\nfor scale-free network modeling, as has been proposed by some authors. The\nresults can also be formulated for non-homogeneous models by making use of a\nrandom sampling procedure over the nodes.\n