Editing Scale-free network (section)

==Estimating the power law exponent==
Estimating the power-law exponent <math>\gamma</math> of a scale-free network is typically done by using the [[Power law#Estimating the exponent from empirical data|maximum likelihood estimation]] with the degrees of a few uniformly sampled nodes.<ref name="Clauset">{{Cite journal |last=Clauset |first=Aaron |author2=Cosma Rohilla Shalizi |author3=M. E. J Newman |year=2009 |title=Power-law distributions in empirical data |journal=SIAM Review |volume=51 |issue=4 |pages=661–703 |arxiv=0706.1062 |bibcode=2009SIAMR..51..661C |doi=10.1137/070710111 |s2cid=9155618}}</ref> However, since uniform sampling does not obtain enough samples from the important heavy-tail of the power law degree distribution, this method can yield a large bias and a variance. It has been recently proposed to sample random friends (i.e., random ends of random links) who are more likely come from the tail of the degree distribution as a result of the [[friendship paradox]].<ref>{{Cite journal |last1=Eom |first1=Young-Ho |last2=Jo |first2=Hang-Hyun |date=2015-05-11 |title=Tail-scope: Using friends to estimate heavy tails of degree distributions in large-scale complex networks |journal=Scientific Reports |volume=5 |issue=1 |page=9752 |doi=10.1038/srep09752 |pmid=25959097 |pmc=4426729 |arxiv=1411.6871 |bibcode=2015NatSR...5.9752E |issn=2045-2322|doi-access=free }}</ref><ref name=":0">{{Cite journal |last1=Nettasinghe |first1=Buddhika |last2=Krishnamurthy |first2=Vikram |date=2021-05-19 |title=Maximum Likelihood Estimation of Power-law Degree Distributions via Friendship Paradox-based Sampling |journal=ACM Transactions on Knowledge Discovery from Data |volume=15 |issue=6 |pages=1–28 |doi=10.1145/3451166 |issn=1556-4681|doi-access=free |arxiv=1908.00310 }}</ref> Theoretically, maximum likelihood estimation with random friends lead to a smaller bias and a smaller variance compared to classical approach based on uniform sampling.<ref name=":0" />