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其中<math>γ</math>是一个常数,被称为幂律指数。这种网络被称为'''[[无标度网络 Scale-free network]]''',它因其特殊的结构和动力学性质而引起人们的关注。<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>然而,最近有一个基于广泛真实数据的综合性研究认为,如果用严格的统计方法,[[无标度网络]]实际上是稀有的。<ref>{{Cite journal|last=Holme|first=Petter|date=2019-03-04|title=Rare and everywhere: Perspectives on scale-free networks|journal=Nature Communications|language=en|volume=10|issue=1|pages=1016|doi=10.1038/s41467-019-09038-8|issn=2041-1723|pmc=6399274|pmid=30833568|bibcode=2019NatCo..10.1016H}}</ref>  
 
其中<math>γ</math>是一个常数,被称为幂律指数。这种网络被称为'''[[无标度网络 Scale-free network]]''',它因其特殊的结构和动力学性质而引起人们的关注。<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>然而,最近有一个基于广泛真实数据的综合性研究认为,如果用严格的统计方法,[[无标度网络]]实际上是稀有的。<ref>{{Cite journal|last=Holme|first=Petter|date=2019-03-04|title=Rare and everywhere: Perspectives on scale-free networks|journal=Nature Communications|language=en|volume=10|issue=1|pages=1016|doi=10.1038/s41467-019-09038-8|issn=2041-1723|pmc=6399274|pmid=30833568|bibcode=2019NatCo..10.1016H}}</ref>  
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一些研究人员对这些发现提出了异议,认为研究中使用的定义过于严格<ref>{{cite journal |last1=Voitalov |first1=Ivan |last2=van der Hoorn |first2=Pim |last3=van der Hofstad |first3=Remco |last4=Krioukov |first4=Dmitri |title=Scale-free networks well done |journal=Physical Review Research |date=18 October 2019 |volume=1 |issue=3 |pages=033034 |doi=10.1103/PhysRevResearch.1.033034|doi-access=free }}</ref> ,其他人则认为,确定度分布的精确函数形式不必要,只需要知道度分布是否为厚尾分布就好<ref>{{Cite journal|last=Holme|first=Petter|date=2019-03-04|title=Rare and everywhere: Perspectives on scale-free networks|journal=Nature Communications|language=en|volume=10|issue=1|pages=1016|doi=10.1038/s41467-019-09038-8|issn=2041-1723|pmc=6399274|pmid=30833568|bibcode=2019NatCo..10.1016H}}</ref> 。对度分布的特定形式的过度解释也受到批评,因为它没有考虑网络如何随时间演化<ref>{{cite journal |last1=Falkenberg |first1=Max |last2=Lee |first2=Jong-Hyeok |last3=Amano |first3=Shun-ichi |last4=Ogawa |first4=Ken-ichiro |last5=Yano |first5=Kazuo |last6=Miyake |first6=Yoshihiro |last7=Evans |first7=Tim S. |last8=Christensen |first8=Kim |title=Identifying time dependence in network growth |journal=Physical Review Research |date=18 June 2020 |volume=2 |issue=2 |pages=023352 |doi=10.1103/PhysRevResearch.2.023352|doi-access=free }}</ref>。
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一些研究人员对这些发现提出了异议,认为研究中使用的定义过于严格<ref>{{cite journal |last1=Voitalov |first1=Ivan |last2=van der Hoorn |first2=Pim |last3=van der Hofstad |first3=Remco |last4=Krioukov |first4=Dmitri |title=Scale-free networks well done |journal=Physical Review Research |date=18 October 2019 |volume=1 |issue=3 |pages=033034 |doi=10.1103/PhysRevResearch.1.033034|doi-access=free }}</ref> ,其他人则认为,没有必要确定度分布的精确函数形式,只需要知道度分布是否为[[厚尾分布]]就好<ref>{{Cite journal|last=Holme|first=Petter|date=2019-03-04|title=Rare and everywhere: Perspectives on scale-free networks|journal=Nature Communications|language=en|volume=10|issue=1|pages=1016|doi=10.1038/s41467-019-09038-8|issn=2041-1723|pmc=6399274|pmid=30833568|bibcode=2019NatCo..10.1016H}}</ref> 。对度分布的特定形式的过度解释也受到批评,因为它没有考虑网络如何随时间演化<ref>{{cite journal |last1=Falkenberg |first1=Max |last2=Lee |first2=Jong-Hyeok |last3=Amano |first3=Shun-ichi |last4=Ogawa |first4=Ken-ichiro |last5=Yano |first5=Kazuo |last6=Miyake |first6=Yoshihiro |last7=Evans |first7=Tim S. |last8=Christensen |first8=Kim |title=Identifying time dependence in network growth |journal=Physical Review Research |date=18 June 2020 |volume=2 |issue=2 |pages=023352 |doi=10.1103/PhysRevResearch.2.023352|doi-access=free }}</ref>。
    
假设一个网络具有度分布<math>P(k)</math>,通过选择一个节点(随机或非随机)跟随一条边到达它的一个邻近点(假设至少有一个邻近点),那么后者具有<math>k</math> 个邻近点的概率不是由<math>P(k)</math>给出的。而是<math>\frac{P(k)}{\langle k \rangle}</math>,这里的<math>{\langle k \rangle}</math>是网络的平均[[度]]。
 
假设一个网络具有度分布<math>P(k)</math>,通过选择一个节点(随机或非随机)跟随一条边到达它的一个邻近点(假设至少有一个邻近点),那么后者具有<math>k</math> 个邻近点的概率不是由<math>P(k)</math>给出的。而是<math>\frac{P(k)}{\langle k \rangle}</math>,这里的<math>{\langle k \rangle}</math>是网络的平均[[度]]。

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