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The more subtle limitation is the commonly held fallacy that vertex centrality indicates the relative importance of vertices. Centrality indices are explicitly designed to produce a ranking which allows indication of the most important vertices. This they do well, under the limitation just noted. They are not designed to measure the influence of nodes in general. Recently, network physicists have begun developing  node influence metrics to address this problem.

The more subtle limitation is the commonly held fallacy that vertex centrality indicates the relative importance of vertices. Centrality indices are explicitly designed to produce a ranking which allows indication of the most important vertices. This they do well, under the limitation just noted. They are not designed to measure the influence of nodes in general. Recently, network physicists have begun developing  node influence metrics to address this problem.

The error is two-fold. Firstly, a ranking only orders vertices by importance, it does not quantify the difference in importance between different levels of the ranking. This may be mitigated by applying Freeman centralization to the centrality measure in question, which provide some insight to the importance of nodes depending on the differences of their centralization scores. Furthermore, Freeman centralization enables one to compare several networks by comparing their highest centralization scores. This approach, however, is seldom seen in practice.

The error is two-fold. Firstly, a ranking only orders vertices by importance, it does not quantify the difference in importance between different levels of the ranking. This may be mitigated by applying Freeman centralization to the centrality measure in question, which provide some insight to the importance of nodes depending on the differences of their centralization scores. Furthermore, Freeman centralization enables one to compare several networks by comparing their highest centralization scores. This approach, however, is seldom seen in practice.

误差是双重的。首先，一个排名只有顺序顶点的重要性，它不量化的重要性之间的不同水平的排名。这可以通过将 Freeman 集中度应用到中心性度量来缓解，这种度量可以根据节点集中度得分的不同来判断节点的重要性。此外，Freeman 集中化使人们能够通过比较几个网络的最高集中化得分来比较它们。然而，这种方法在实践中很少见到。

误差是双重的。首先，一个排名只根据顶点的重要性排序，它并不对节点重要性的不同水平进行量化区分。这可以通过将 Freeman （自由人）集中度应用到中心性度量来缓解，这种度量可以根据节点集中度得分的不同来判断节点的重要性。此外，Freeman （自由人）集中化使人们能够通过比较几个网络的最高集中化得分来比较它们。然而，这种方法在实践中很少见到。

Secondly, the features which (correctly) identify the most important vertices in a given network/application do not necessarily generalize to the remaining vertices.  

Secondly, the features which (correctly) identify the most important vertices in a given network/application do not necessarily generalize to the remaining vertices.  

其次，(正确地)识别给定网络/应用程序中最重要顶点的特征并不一定泛化到其余顶点。

其次，用以(正确地)识别给定网络/应用程序中最重要顶点的特征并不一定可推广到其余顶点。

For the majority of other network nodes the rankings may be meaningless.<ref name="Lawyer2015" /><ref name="daSilva2012">{{cite journal | last1=da Silva|first1=Renato |last2=Viana|first2=Matheus|last3=da F. Costa |first3=Luciano| title=Predicting epidemic outbreak from individual features of the spreaders| journal=J. Stat. Mech.: Theory Exp. | year=2012|volume=2012|pages=P07005|number=7 | doi=10.1088/1742-5468/2012/07/p07005|arxiv=1202.0024|bibcode=2012JSMTE..07..005A}}</ref><ref name="Bauer2012">{{cite journal | last1=Bauer|first1=Frank | last2=Lizier|first2=Joseph|title=Identifying influential spreaders and efficiently estimating infection numbers in epidemic models: A walk counting approach| journal=Europhys Lett | year=2012| volume=99| pages=68007|number=6 | doi=10.1209/0295-5075/99/68007|arxiv=1203.0502|bibcode=2012EL.....9968007B}}</ref><ref name="Sikic2013">{{ cite journal| last1= Sikic| first1=Mile|last2=Lancic|first2=Alen|last3=Antulov-Fantulin|first3=Nino|last4=Stefanic|first4=Hrvoje| title = Epidemic centrality -- is there an underestimated epidemic impact of network peripheral nodes? |journal = The European Physical Journal B |volume=86 |number=10 |pages=1–13 |year=2013 | doi=10.1140/epjb/e2013-31025-5|arxiv=1110.2558 | bibcode=2013EPJB...86..440S}}</ref> This explains why, for example, only the first few results of a Google image search appear in a reasonable order. The pagerank is a highly unstable measure, showing frequent rank reversals after small adjustments of the jump parameter.<ref name="Ghoshal2011">{{cite journal | last1=Ghoshal | first1= G. | last2= Barabsi |first2= A L | title = Ranking stability and super-stable nodes in complex networks. | journal = Nat Commun | volume =2 | page = 394| year= 2011 | doi=10.1038/ncomms1396 | pmid= 21772265 | bibcode=2011NatCo...2..394G | doi-access= free }}</ref>

For the majority of other network nodes the rankings may be meaningless.<ref name="Lawyer2015" /><ref name="daSilva2012">{{cite journal | last1=da Silva|first1=Renato |last2=Viana|first2=Matheus|last3=da F. Costa |first3=Luciano| title=Predicting epidemic outbreak from individual features of the spreaders| journal=J. Stat. Mech.: Theory Exp. | year=2012|volume=2012|pages=P07005|number=7 | doi=10.1088/1742-5468/2012/07/p07005|arxiv=1202.0024|bibcode=2012JSMTE..07..005A}}</ref><ref name="Bauer2012">{{cite journal | last1=Bauer|first1=Frank | last2=Lizier|first2=Joseph|title=Identifying influential spreaders and efficiently estimating infection numbers in epidemic models: A walk counting approach| journal=Europhys Lett | year=2012| volume=99| pages=68007|number=6 | doi=10.1209/0295-5075/99/68007|arxiv=1203.0502|bibcode=2012EL.....9968007B}}</ref><ref name="Sikic2013">{{ cite journal| last1= Sikic| first1=Mile|last2=Lancic|first2=Alen|last3=Antulov-Fantulin|first3=Nino|last4=Stefanic|first4=Hrvoje| title = Epidemic centrality -- is there an underestimated epidemic impact of network peripheral nodes? |journal = The European Physical Journal B |volume=86 |number=10 |pages=1–13 |year=2013 | doi=10.1140/epjb/e2013-31025-5|arxiv=1110.2558 | bibcode=2013EPJB...86..440S}}</ref> This explains why, for example, only the first few results of a Google image search appear in a reasonable order. The pagerank is a highly unstable measure, showing frequent rank reversals after small adjustments of the jump parameter.<ref name="Ghoshal2011">{{cite journal | last1=Ghoshal | first1= G. | last2= Barabsi |first2= A L | title = Ranking stability and super-stable nodes in complex networks. | journal = Nat Commun | volume =2 | page = 394| year= 2011 | doi=10.1038/ncomms1396 | pmid= 21772265 | bibcode=2011NatCo...2..394G | doi-access= free }}</ref>