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(or [[Poisson distribution|Poisson]] in the limit of large ''n'', if the average degree <math>\langle k\rangle=p(n-1)</math> is held fixed). Most networks in the real world, however, have degree distributions very different from this. Most are highly [[Skewness|right-skewed]], meaning that a large majority of nodes have low degree but a small number, known as "hubs", have high degree. Some networks, notably the Internet, the [[world wide web]], and some social networks were argued to have degree distributions that approximately follow a [[power law]]: <math>
P(k)\sim k^{-\gamma}
</math>, where ''γ'' is a constant. Such networks are called [[scale-free networks]] and have attracted particular attention for their structural and dynamical properties.<ref name="BA">{{cite journal | last=Barabási | first=Albert-László | last2=Albert | first2=Réka | title=Emergence of Scaling in Random Networks | journal=Science | volume=286 | issue=5439 | date=1999-10-15 | issn=0036-8075 | doi=10.1126/science.286.5439.509 | pages=509–512| pmid=10521342 | arxiv=cond-mat/9910332 | bibcode=1999Sci...286..509B }}</ref><ref name="AB">{{cite journal | last=Albert | first=Réka | last2=Barabási | first2=Albert-László | title=Topology of Evolving Networks: Local Events and Universality | journal=Physical Review Letters | volume=85 | issue=24 | date=2000-12-11 | issn=0031-9007 | doi=10.1103/physrevlett.85.5234 | pages=5234–5237| pmid=11102229 | arxiv=cond-mat/0005085 | bibcode=2000PhRvL..85.5234A | hdl=2047/d20000695 | url=https://repository.library.northeastern.edu/files/neu:331099/fulltext.pdf }}</ref><ref name="Doro">{{cite journal | last=Dorogovtsev | first=S. N. | last2=Mendes | first2=J. F. F. | last3=Samukhin | first3=A. N. | title=Size-dependent degree distribution of a scale-free growing network | journal=Physical Review E | volume=63 | issue=6 | date=2001-05-21 | issn=1063-651X | doi=10.1103/physreve.63.062101 | page=062101| pmid=11415146 |arxiv=cond-mat/0011115| bibcode=2001PhRvE..63f2101D }}</ref><ref name="PSY">{{cite journal|title=Scale-free behavior of networks with the copresence of preferential and uniform attachment rules|journal=Physica D: Nonlinear Phenomena|year=2018|first=Angelica |last=Pachon |first2=Laura |last2=Sacerdote |first3=Shuyi |last3=Yang |volume=371|pages=1–12|doi=10.1016/j.physd.2018.01.005|arxiv=1704.08597|bibcode=2018PhyD..371....1P}}</ref>
== Excess degree distribution ==
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</math> is <math>
q(k)
</math> which is called the ''excess degree'' of that node. In the [[configuration model]], which correlations between the nodes have been ignored and every node is assumed to be connected to any other nodes in the network with the same probability, the excess degree distribution can be found as:<ref name=":0" />
<math>
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</math>
And in general:<ref name=":0" />
* <math>
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