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第392行： − 根据 Alex Lopez-Ortiz 的说法，在1986年到1994年的3个赛季中，所有的费尔德斯和奈望林纳奖冠军的 erd 数量最多不超过9。+ − + − 早期数学家发表的论文比现代数学家少，联合发表的论文也更少。根据出版资格标准的不同，已知最早拥有有限 erd 数目的人要么是安托万-洛朗·德·拉瓦锡(出生于1743年，erd 数目13) ，要么是理查德·戴德金(出生于1831年，erd 数目7) ，要么是费迪南德·格奥尔格·弗罗贝尼乌斯(出生于1849年，erd 数目3)。+ − + − Martin Tompa 提出了 erd 数问题的一个有向图版本，通过定向协作图的边，从字母顺序的前作者到字母顺序的后作者，并定义单调的作者 erd 数为从 Erdős 到作者的最长路径的长度。他找到了一条长度为12的路径。+ 第416行：
第416行： − 此外，迈克尔 · 巴尔还提出了“合理的 erd 数字” ，概括了这样一个观点，即一个与 erd s 共同撰写了 p 篇论文的人应该被赋予 erd s 1/p。从第二种合作多重图(虽然他也有办法处理第一种情况)ーー两个数学家为他们生产的每一张合作论文画一条边ーー形成一个电网络，每条边上有一个一欧姆电阻器。两个节点之间的总电阻表示这两个节点的“关闭”程度。+ − + − 有人认为，”对于单个研究人员来说，erd 数字这样的衡量标准反映了网络的结构特性，而 h-index 则反映了出版物的引用影响” ，”人们很容易相信，在合作网络中的排名应该考虑到这两项措施，以产生一个现实的和可接受的排名+ − + − 2004年，数学家威廉 · 托齐尔(William Tozier)在 eBay 上拍卖了一幅共同作者的作品，给买家提供了厄德数为5的作品。一位西班牙数学家以1031美元的价格成交，但是这位数学家并不打算出价，只是为了阻止这个他认为是嘲弄的东西。+
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According to Alex Lopez-Ortiz, all the Fields and Nevanlinna prize winners during the three cycles in 1986 to 1994 have Erdős numbers of at most 9.
According to Alex Lopez-Ortiz, all the Fields and Nevanlinna prize winners during the three cycles in 1986 to 1994 have Erdős numbers of at most 9.
根据亚历克斯·洛佩兹·奥尔蒂斯Alex Lopez-Ortiz的说法，在1986年至1994年的三个周期中，所有费尔兹奖Fields和内凡琳娜奖Nevanlinna prize得主的埃尔德什数最多为9。
Earlier mathematicians published fewer papers than modern ones, and more rarely published jointly written papers. The earliest person known to have a finite Erdős number is either [[Antoine Lavoisier]] (born 1743, Erdős number 13), [[Richard Dedekind]] (born 1831, Erdős number 7), or [[Ferdinand Georg Frobenius]] (born 1849, Erdős number 3), depending on the standard of publication eligibility.<ref>{{cite web|url=http://www.oakland.edu/enp/erdpaths |title=Paths to Erdös - The Erdös Number Project- Oakland University|work=oakland.edu}}</ref>
Earlier mathematicians published fewer papers than modern ones, and more rarely published jointly written papers. The earliest person known to have a finite Erdős number is either [[Antoine Lavoisier]] (born 1743, Erdős number 13), [[Richard Dedekind]] (born 1831, Erdős number 7), or [[Ferdinand Georg Frobenius]] (born 1849, Erdős number 3), depending on the standard of publication eligibility.
Earlier mathematicians published fewer papers than modern ones, and more rarely published jointly written papers. The earliest person known to have a finite Erdős number is either Antoine Lavoisier (born 1743, Erdős number 13), Richard Dedekind (born 1831, Erdős number 7), or Ferdinand Georg Frobenius (born 1849, Erdős number 3), depending on the standard of publication eligibility.
Earlier mathematicians published fewer papers than modern ones, and more rarely published jointly written papers. The earliest person known to have a finite Erdős number is either Antoine Lavoisier (born 1743, Erdős number 13), Richard Dedekind (born 1831, Erdős number 7), or Ferdinand Georg Frobenius (born 1849, Erdős number 3), depending on the standard of publication eligibility.
较早的数学家发表的论文通常少于现代的，而且很少发表联合论文。已知拥有有限埃尔德什数的最早学者是Antoine Lavoisier（生于1743年，埃尔德什数为13），Richard Dedekind（生于1831年，埃尔德什数为7）或Ferdinand Georg Frobenius（生于1849年，埃尔德什数为3），具体取决于出版物资格标准。
Martin Tompa<ref>{{cite journal|last=Tompa|first=Martin|title=Figures of merit|journal=ACM SIGACT News|volume=20|issue=1|pages=62–71|year=1989|doi=10.1145/65780.65782}} {{cite journal|last=Tompa|first= Martin|title=Figures of merit: the sequel|journal=ACM SIGACT News|volume=21|issue=4|pages=78–81|year=1990|doi=10.1145/101371.101376}}</ref> proposed a [[directed graph]] version of the Erdős number problem, by orienting edges of the collaboration graph from the alphabetically earlier author to the alphabetically later author and defining the ''monotone Erdős number'' of an author to be the length of a [[longest path]] from Erdős to the author in this directed graph. He finds a path of this type of length 12.
Martin Tompa proposed a [[directed graph]] version of the Erdős number problem, by orienting edges of the collaboration graph from the alphabetically earlier author to the alphabetically later author and defining the ''monotone Erdős number'' of an author to be the length of a [[longest path]] from Erdős to the author in this directed graph. He finds a path of this type of length 12.
Martin Tompa proposed a directed graph version of the Erdős number problem, by orienting edges of the collaboration graph from the alphabetically earlier author to the alphabetically later author and defining the monotone Erdős number of an author to be the length of a longest path from Erdős to the author in this directed graph. He finds a path of this type of length 12.
Martin Tompa proposed a directed graph version of the Erdős number problem, by orienting edges of the collaboration graph from the alphabetically earlier author to the alphabetically later author and defining the monotone Erdős number of an author to be the length of a longest path from Erdős to the author in this directed graph. He finds a path of this type of length 12.
马丁·汤帕Martin Tompa提出了埃尔德什数问题的有向图版本，通过定向协作图，将字母顺序更早的作者到字母顺序更晚的作者进行排列，并将作者的单调埃尔德什数定义为该有向图中从埃尔德什到作者的最长路径的长度。他发现这种路径长度为12。
Also, Michael Barr suggests "rational Erdős numbers", generalizing the idea that a person who has written p joint papers with Erdős should be assigned Erdős number 1/p. From the collaboration multigraph of the second kind (although he also has a way to deal with the case of the first kind)—with one edge between two mathematicians for each joint paper they have produced—form an electrical network with a one-ohm resistor on each edge. The total resistance between two nodes tells how "close" these two nodes are.
Also, Michael Barr suggests "rational Erdős numbers", generalizing the idea that a person who has written p joint papers with Erdős should be assigned Erdős number 1/p. From the collaboration multigraph of the second kind (although he also has a way to deal with the case of the first kind)—with one edge between two mathematicians for each joint paper they have produced—form an electrical network with a one-ohm resistor on each edge. The total resistance between two nodes tells how "close" these two nodes are.
另外，迈克尔·巴尔（Michael Barr）曾建议使用“合理的埃尔德什数”，通俗的说就是与埃尔德共同撰写过p篇论文的人应被分配埃尔德什数的1/p。根据第二种的协作多重图（尽管他也有办法处理第一种情况），即在他们所合著的每篇联合论文中，两个数学家之间都有一条边，这个边缘上都有一个1欧姆电阻器的电网。两个节点之间的总电阻表明这两个节点有多“相近”。
It has been argued that "for an individual researcher, a measure such as Erdős number captures the structural properties of [the] network whereas the [[h-index|''h''-index]] captures the citation impact of the publications," and that "One can be easily convinced that ranking in coauthorship networks should take into account both measures to generate a realistic and acceptable ranking."<ref name=Dixit>Kashyap Dixit, S Kameshwaran, Sameep Mehta, Vinayaka Pandit, N Viswanadham, ''[http://domino.research.ibm.com/library/cyberdig.nsf/papers/2B600A90C54E51B18525755800283D37/$File/RR_ranking.pdf Towards simultaneously exploiting structure and outcomes in interaction networks for node ranking]'', IBM Research Report R109002, February 2009; also appeared as {{Cite journal | doi = 10.1145/1871437.1871470| pmc = | pmid = | last1 = Kameshwaran | first1 = S. | last2 = Pandit | first2 = V. | last3 = Mehta | first3 = S. | last4 = Viswanadham | first4 = N. | last5 = Dixit | first5 = K. | title = Outcome aware ranking in interaction networks | pages = 229–238| year = 2010 | isbn = 978-1-4503-0099-5| journal = Proceedings of the 19th ACM international conference on Information and knowledge management (CIKM '10)| url = http://www.cse.iitd.ernet.in/%7Epandit/cikm_camera_ready.pdf}}</ref>
It has been argued that "for an individual researcher, a measure such as Erdős number captures the structural properties of [the] network whereas the [[h-index|''h''-index]] captures the citation impact of the publications," and that "One can be easily convinced that ranking in coauthorship networks should take into account both measures to generate a realistic and acceptable ranking."
It has been argued that "for an individual researcher, a measure such as Erdős number captures the structural properties of [the] network whereas the h-index captures the citation impact of the publications," and that "One can be easily convinced that ranking in coauthorship networks should take into account both measures to generate a realistic and acceptable ranking."
It has been argued that "for an individual researcher, a measure such as Erdős number captures the structural properties of [the] network whereas the h-index captures the citation impact of the publications," and that "One can be easily convinced that ranking in coauthorship networks should take into account both measures to generate a realistic and acceptable ranking."
有人争辩说：“对于独立研究人员而言，诸如埃尔德什数之类的量度可以捕获网络的结构特性，而h指数则可以捕获出版物的引文影响。” 并且“可以很容易地使人相信，共同作者网络中的排名应该同时考虑到两种方法，以产生现实且可接受的排名。”
In 2004 William Tozier, a mathematician with an Erdős number of 4, auctioned off a co-authorship on [[eBay]], hence providing the buyer with an Erdős number of 5. The winning bid of $1031 was posted by a Spanish mathematician, who however did not intend to pay but just placed the bid to stop what he considered a mockery.<ref>Clifford A. Pickover: ''A Passion for Mathematics: Numbers, Puzzles, Madness, Religion, and the Quest for Reality''. Wiley, 2011, {{ISBN|9781118046074}}, S. 33 ({{Google books|03CVDsZSBIcC|excerpt|page=33}})</ref><ref>{{cite journal | last1 = Klarreich | first1 = Erica | year = 2004 | title = Theorem for Sale | journal = Science News | volume = 165 | issue = 24| pages = 376–377 | jstor=4015267}}</ref>
In 2004 William Tozier, a mathematician with an Erdős number of 4, auctioned off a co-authorship on [[eBay]], hence providing the buyer with an Erdős number of 5. The winning bid of $1031 was posted by a Spanish mathematician, who however did not intend to pay but just placed the bid to stop what he considered a mockery.
In 2004 William Tozier, a mathematician with an Erdős number of 4, auctioned off a co-authorship on eBay, hence providing the buyer with an Erdős number of 5. The winning bid of $1031 was posted by a Spanish mathematician, who however did not intend to pay but just placed the bid to stop what he considered a mockery.
In 2004 William Tozier, a mathematician with an Erdős number of 4, auctioned off a co-authorship on eBay, hence providing the buyer with an Erdős number of 5. The winning bid of $1031 was posted by a Spanish mathematician, who however did not intend to pay but just placed the bid to stop what he considered a mockery.
2004年，数学家埃尔德什数为4的William Tozier在eBay上拍卖了合著者，因此为买家提供了埃尔德什数为5的机会。一位西班牙数学家发布了1031美元的中标价格，不过他并不打算付款，而只是提出了中标要求，以阻止他认为是嘲弄的行为。
==Variations==
==Variations==