# 六度分隔理论

An arctic food web showing the number of degrees of separation of the animals from phyto-plankton – for example, capelin are 4 connections away from phyto-plankton

Six degrees of separation is the idea that all people on average are six, or fewer, social connections away from each other. Also known as the 6 Handshakes rule. As a result, a chain of "a friend of a friend" statements can be made to connect any two people in a maximum of six steps. It was originally set out by Frigyes Karinthy in 1929 and popularized in an eponymous 1990 play written by John Guare. It is sometimes generalized to the average social distance being logarithmic in the size of the population.

Six degrees of separation is the idea that all people on average are six, or fewer, social connections away from each other. Also known as the 6 Handshakes rule. As a result, a chain of "a friend of a friend" statements can be made to connect any two people in a maximum of six steps. It was originally set out by Frigyes Karinthy in 1929 and popularized in an eponymous 1990 play written by John Guare. It is sometimes generalized to the average social distance being logarithmic in the size of the population.

## Early conceptions

### Shrinking world

Theories on optimal design of cities, city traffic flows, neighborhoods, and demographics were in vogue after World War I. These[citation needed] conjectures were expanded in 1929 by Hungarian author Frigyes Karinthy, who published a volume of short stories titled Everything is Different. One of these pieces was titled "Chains," or "Chain-Links." The story investigated模板:Snd in abstract, conceptual, and fictional terms模板:Snd many of the problems that would captivate future generations of mathematicians, sociologists, and physicists within the field of network theory.[1][2] Due to technological advances in communications and travel, friendship networks could grow larger and span greater distances. In particular, Karinthy believed that the modern world was 'shrinking' due to this ever-increasing connectedness of human beings. He posited that despite great physical distances between the globe's individuals, the growing density of human networks made the actual social distance far smaller.[3]

Theories on optimal design of cities, city traffic flows, neighborhoods, and demographics were in vogue after World War I. These conjectures were expanded in 1929 by Hungarian author Frigyes Karinthy, who published a volume of short stories titled Everything is Different. One of these pieces was titled "Chains," or "Chain-Links." The story investigated in abstract, conceptual, and fictional terms many of the problems that would captivate future generations of mathematicians, sociologists, and physicists within the field of network theory.

As a result of this hypothesis, Karinthy's characters believed that any two individuals could be connected through at most five acquaintances. In his story, the characters create a game out of this notion. He wrote:

As a result of this hypothesis, Karinthy's characters believed that any two individuals could be connected through at most five acquaintances. In his story, the characters create a game out of this notion. He wrote:

A fascinating game grew out of this discussion. One of us suggested performing the following experiment to prove that the population of the Earth is closer together now than they have ever been before. We should select any person from the 1.5 billion inhabitants of the Earth – anyone, anywhere at all. He bet us that, using no more than five individuals, one of whom is a personal acquaintance, he could contact the selected individual using nothing except the network of personal acquaintances.[4]

A fascinating game grew out of this discussion. One of us suggested performing the following experiment to prove that the population of the Earth is closer together now than they have ever been before. We should select any person from the 1.5 billion inhabitants of the Earth – anyone, anywhere at all. He bet us that, using no more than five individuals, one of whom is a personal acquaintance, he could contact the selected individual using nothing except the network of personal acquaintances.

This idea both directly and indirectly influenced a great deal of early thought on social networks. Karinthy has been regarded as the originator of the notion of six degrees of separation.[2]

This idea both directly and indirectly influenced a great deal of early thought on social networks. Karinthy has been regarded as the originator of the notion of six degrees of separation.

A related theory deals with the quality of connections, rather than their existence. The theory of three degrees of influence was created by Nicholas A. Christakis and James H. Fowler.[citation needed]

A related theory deals with the quality of connections, rather than their existence. The theory of three degrees of influence was created by Nicholas A. Christakis and James H. Fowler.

### Small world

Michael Gurevich conducted seminal work in his empirical study of the structure of social networks in his 1961 Massachusetts Institute of Technology PhD dissertation under Ithiel de Sola Pool.[5] Mathematician Manfred Kochen, an Austrian who had been involved in urban design, extrapolated these empirical results in a mathematical manuscript, Contacts and Influences,[6] concluding that in a U.S.-sized population without social structure, "it is practically certain that any two individuals can contact one another by means of at most two intermediaries. In a [socially] structured population it is less likely but still seems probable. And perhaps for the whole world's population, probably only one more bridging individual should be needed." They subsequently constructed Monte Carlo simulations based on Gurevich's data, which recognized that both weak and strong acquaintance links are needed to model social structure. The simulations, carried out on the relatively limited computers of 1973, were nonetheless able to predict that a more realistic three degrees of separation existed across the U.S. population, foreshadowing the findings of American psychologist Stanley Milgram.[citation needed]

Michael Gurevich conducted seminal work in his empirical study of the structure of social networks in his 1961 Massachusetts Institute of Technology PhD dissertation under Ithiel de Sola Pool. Mathematician Manfred Kochen, an Austrian who had been involved in urban design, extrapolated these empirical results in a mathematical manuscript, Contacts and Influences, concluding that in a U.S.-sized population without social structure, "it is practically certain that any two individuals can contact one another by means of at most two intermediaries. In a [socially] structured population it is less likely but still seems probable. And perhaps for the whole world's population, probably only one more bridging individual should be needed." They subsequently constructed Monte Carlo simulations based on Gurevich's data, which recognized that both weak and strong acquaintance links are needed to model social structure. The simulations, carried out on the relatively limited computers of 1973, were nonetheless able to predict that a more realistic three degrees of separation existed across the U.S. population, foreshadowing the findings of American psychologist Stanley Milgram.

1961年，迈克尔 · 古列维奇在麻省理工学院的 istiel de Sola Pool 博士论文中对社交网络的结构进行了实证研究。数学家 Manfred Kochen 是一位奥地利人，曾经参与城市设计，他将这些经验性的结果以数学手稿《联系与影响》的形式推断出，在一个没有社会结构的美国大规模人口中，“实际上可以肯定的是，任何两个个体至多可以通过两个中间人进行联系。在一个(社会)结构化的人群中，这种情况不太可能发生，但似乎仍然是可能的。或许对于全世界的人口而言，也许只需要再增加一个连接个体。”他们随后基于 Gurevich 的数据构建了蒙特卡罗模拟，该模拟认识到为社会结构建模既需要弱的熟人联系，也需要强的熟人联系。1973年在相对有限的计算机上进行的模拟，尽管如此，仍然能够预测在美国人口中存在更为现实的三度分离，这预示着美国心理学家斯坦利 · 米尔格拉姆的发现。

Milgram continued Gurevich's experiments in acquaintanceship networks at Harvard University in Cambridge, Massachusetts, U.S. Kochen and de Sola Pool's manuscript, Contacts and Influences,[7] was conceived while both were working at the University of Paris in the early 1950s, during a time when Milgram visited and collaborated in their research. Their unpublished manuscript circulated among academics for over 20 years before publication in 1978. It formally articulated the mechanics of social networks, and explored the mathematical consequences of these (including the degree of connectedness). The manuscript left many significant questions about networks unresolved, and one of these was the number of degrees of separation in actual social networks. Milgram took up the challenge on his return from Paris, leading to the experiments reported in The Small World Problem [8] in popular science journal Psychology Today, with a more rigorous version of the paper appearing in Sociometry two years later.[9] The Psychology Today article generated enormous publicity for the experiments, which are well known today, long after much of the formative work has been forgotten.

Milgram continued Gurevich's experiments in acquaintanceship networks at Harvard University in Cambridge, Massachusetts, U.S. Kochen and de Sola Pool's manuscript, Contacts and Influences, was conceived while both were working at the University of Paris in the early 1950s, during a time when Milgram visited and collaborated in their research. Their unpublished manuscript circulated among academics for over 20 years before publication in 1978. It formally articulated the mechanics of social networks, and explored the mathematical consequences of these (including the degree of connectedness). The manuscript left many significant questions about networks unresolved, and one of these was the number of degrees of separation in actual social networks. Milgram took up the challenge on his return from Paris, leading to the experiments reported in The Small World Problem in popular science journal Psychology Today, with a more rigorous version of the paper appearing in Sociometry two years later. The Psychology Today article generated enormous publicity for the experiments, which are well known today, long after much of the formative work has been forgotten.

Milgram's article made famous[8] his 1967 set of experiments to investigate de Sola Pool and Kochen's "small world problem." Mathematician Benoit Mandelbrot, born in Warsaw, growing up in Poland then France, was aware of the Statist rule of thumb, and was also a colleague of de Sola Pool, Kochen and Milgram at the University of Paris during the early 1950s (Kochen brought Mandelbrot to work at the Institute for Advanced Study and later IBM in the U.S.). This circle of researchers was fascinated by the interconnectedness and "social capital" of human networks. Milgram's study results showed that people in the United States seemed to be connected by approximately three friendship links, on average, without speculating on global linkages; he never actually used the term "six degrees of separation." Since the Psychology Today article gave the experiments wide publicity, Milgram, Kochen, and Karinthy all had been incorrectly attributed as the origin of the notion of six degrees; the most likely popularizer of the term "six degrees of separation" would be John Guare, who attributed the value '6' to Marconi.[10]

### Continued research: Small World Project

In 2003, Columbia University conducted an analogous experiment on social connectedness amongst Internet email users. Their effort was named the Columbia Small World Project, and included 24,163 e-mail chains, aimed at 18 targets from 13 countries.[11] Almost 100,000 people registered, but only 384 (0.4%) reached the final target. Amongst the successful chains, while shorter lengths were more common some reached their target after only 7, 8, 9 or 10 steps. Dodds et al. noted that participants (all of whom volunteers) were strongly biased towards existing models of Internet users[Note 1] and that connectedness based on professional ties was much stronger than those within families or friendships. The authors cite "lack of interest" as the predominating factor in the high attrition rate,[Note 2] a finding consistent with earlier studies.[12]

In 2003, Columbia University conducted an analogous experiment on social connectedness amongst Internet email users. Their effort was named the Columbia Small World Project, and included 24,163 e-mail chains, aimed at 18 targets from 13 countries. Almost 100,000 people registered, but only 384 (0.4%) reached the final target. Amongst the successful chains, while shorter lengths were more common some reached their target after only 7, 8, 9 or 10 steps. Dodds et al. noted that participants (all of whom volunteers) were strongly biased towards existing models of Internet users{{#tag:ref|"More than half of all participants resided in North America and were middle class, professional, college educated, and Christian, reflecting commonly held notions of the Internet-using population"

2003年，哥伦比亚大学在互联网电子邮件用户之间进行了一个类似的社会联系实验。他们的努力被命名为“哥伦比亚小世界项目”(Columbia Small World Project) ，其中包括24,163个电子邮件链，目标是来自13个国家的18个目标。近10万人注册，但只有384人(0.4%)达到了最终目标。在成功的连锁店中，较短的长度更常见，有些只经过7、8、9或10步就达到了目标。等人。“超过一半的参与者居住在北美，属于中产阶级、专业人士、受过大学教育的人和基督徒，这反映了人们对使用互联网人群的普遍看法。”

## Research

However, detractors argue that Milgram's experiment did not demonstrate such a link, and the "six degrees" claim has been decried as an "academic urban myth". Also, the existence of isolated groups of humans, for example the Korubo and other native Brazilian populations, would tend to invalidate the strictest interpretation of the hypothesis.

Several studies, such as Milgram's small world experiment, have been conducted to measure this connectedness empirically. The phrase "six degrees of separation" is often used as a synonym for the idea of the "small world" phenomenon.[13]

However, detractors argue that Milgram's experiment did not demonstrate such a link,[14] and the "six degrees" claim has been decried as an "academic urban myth".[12][15] Also, the existence of isolated groups of humans, for example the Korubo and other native Brazilian populations,[16] would tend to invalidate the strictest interpretation of the hypothesis.

In 2001, Duncan Watts, a professor at Columbia University, attempted to recreate Milgram's experiment on the Internet, using an e-mail message as the "package" that needed to be delivered, with 48,000 senders and 19 targets (in 157 countries). Watts found that the average (though not maximum) number of intermediaries was around six.

2001年，哥伦比亚大学(Columbia University)教授邓肯•沃茨(Duncan Watts)试图在互联网上重现米尔格拉姆的实验，他使用一封电子邮件作为需要投递的“包裹” ，共有4.8万个发件人和19个目标(分布在157个国家)。Watts 发现，中间商的平均数量(虽然不是最大数量)约为6个。

A 2007 study by Jure Leskovec and Eric Horvitz examined a data set of instant messages composed of 30 billion conversations among 240 million people. They found the average path length among Microsoft Messenger users to be 6.

2007年，Jure Leskovec 和 Eric Horvitz 进行了一项研究，调查了2.4亿人的300亿次对话，组成了一个即时消息数据集。他们发现微软信使用户的平均路径长度为6。

### Computer networks

In 2001, Duncan Watts, a professor at Columbia University, attempted to recreate Milgram's experiment on the Internet, using an e-mail message as the "package" that needed to be delivered, with 48,000 senders and 19 targets (in 157 countries). Watts found that the average (though not maximum) number of intermediaries was around six.[17]

It has been suggested by some commentators that interlocking networks of computer mediated lateral communication could diffuse single messages to all interested users worldwide as per the 6 degrees of separation principle via Information Routing Groups, which are networks specifically designed to exploit this principle and lateral diffusion.

A 2007 study by Jure Leskovec and Eric Horvitz examined a data set of instant messages composed of 30 billion conversations among 240 million people. They found the average path length among Microsoft Messenger users to be 6.[18]

It has been suggested by some commentators[19] that interlocking networks of computer mediated lateral communication could diffuse single messages to all interested users worldwide as per the 6 degrees of separation principle via Information Routing Groups, which are networks specifically designed to exploit this principle and lateral diffusion.

Bakhshandeh et al. have addressed the search problem of identifying the degree of separation between two users in social networks such as Twitter. They have introduced new search techniques to provide optimal or near optimal solutions. The experiments are performed using Twitter, and they show an improvement of several orders of magnitude over greedy approaches. Their optimal algorithm finds an average degree of separation of 3.43 between two random Twitter users, requiring an average of only 67 requests for information over the Internet to Twitter. A near-optimal solution of length 3.88 can be found by making an average of 13.3 requests.

### An optimal algorithm to calculate degrees of separation in social networks

Bakhshandeh et al.[20] have addressed the search problem of identifying the degree of separation between two users in social networks such as Twitter. They have introduced new search techniques to provide optimal or near optimal solutions. The experiments are performed using Twitter, and they show an improvement of several orders of magnitude over greedy approaches. Their optimal algorithm finds an average degree of separation of 3.43 between two random Twitter users, requiring an average of only 67 requests for information over the Internet to Twitter. A near-optimal solution of length 3.88 can be found by making an average of 13.3 requests.

No longer limited strictly to academic or philosophical thinking, the notion of six degrees recently has become influential throughout popular culture. Further advances in communication technology – and particularly the Internet – have drawn great attention to social networks and human interconnectedness. As a result, many popular media sources have addressed the term. The following provide a brief outline of the ways such ideas have shaped popular culture.

## Popularization

No longer limited strictly to academic or philosophical thinking, the notion of six degrees recently has become influential throughout popular culture. Further advances in communication technology – and particularly the Internet – have drawn great attention to social networks and human interconnectedness. As a result, many popular media sources have addressed the term. The following provide a brief outline of the ways such ideas have shaped popular culture.

### Popularization of offline practice

American playwright John Guare wrote a play in 1990 and released a 1993 film that popularized it; it is Guare's most widely known work. The play ruminates upon the idea that any two individuals are connected by at most five others. As one of the characters states:

#### John Guare's Six Degrees of Separation

< 我们的目标是什么 >

American playwright John Guare wrote a play in 1990 and released a 1993 film that popularized it; it is Guare's most widely known work. [citation needed] The play ruminates upon the idea that any two individuals are connected by at most five others. As one of the characters states:

I read somewhere that everybody on this planet is separated by only six other people. Six degrees of separation between us and everyone else on this planet. The President of the United States, a gondolier in Venice, just fill in the names. I find it A) extremely comforting that we're so close, and B) like Chinese water torture that we're so close because you have to find the right six people to make the right connection... I am bound to everyone on this planet by a trail of six people.

I read somewhere that everybody on this planet is separated by only six other people. Six degrees of separation between us and everyone else on this planet. The President of the United States, a gondolier in Venice, just fill in the names. I find it A) extremely comforting that we're so close, and B) like Chinese water torture that we're so close because you have to find the right six people to make the right connection... I am bound to everyone on this planet by a trail of six people.[21]

Guare, in interviews, attributed his awareness of the "six degrees" to Marconi. Although this idea had been circulating in various forms for decades, it is Guare's piece that is most responsible for popularizing the phrase "six degrees of separation." Following Guare's lead, many future television and film sources would later incorporate the notion into their stories.

J. J. Abrams, the executive producer of television series Six Degrees and Lost, played the role of Doug in the film adaptation of this play. Many of the play's themes are apparent in his television shows (see below).

J · j · 艾布拉姆斯，电视连续剧《六度》和《迷失》的执行制片人，在这部改编剧本的电影中扮演道格的角色。该剧的许多主题在他的电视节目中都很明显。

Guare, in interviews, attributed his awareness of the "six degrees" to Marconi.[citation needed] Although this idea had been circulating in various forms for decades, it is Guare's piece that is most responsible for popularizing the phrase "six degrees of separation."[citation needed] Following Guare's lead, many future television and film sources would later incorporate the notion into their stories.[citation needed]

J. J. Abrams, the executive producer of television series Six Degrees and Lost, played the role of Doug in the film adaptation of this play.[citation needed] Many of the play's themes are apparent in his television shows (see below).[citation needed]

The game "Six Degrees of Kevin Bacon" was invented as a play on the concept: the goal is to link any actor to Kevin Bacon through no more than six connections, where two actors are connected if they have appeared in a movie or commercial together. It was created by three students at Albright College in Pennsylvania, who came up with the concept while watching Footloose. On September 13, 2012, Google made it possible to search for any given actor's 'Bacon Number' through their search engine.

《凯文 · 培根的六度》这个游戏是根据这个概念发明的: 目标是通过不超过六个连接将任何一个演员与凯文 · 培根联系起来，如果两个演员一起出现在电影或商业广告中，他们就会被连接起来。它是由宾夕法尼亚州奥尔布赖特学院的三个学生在观看《浑身是劲》时想出来的。2012年9月13日，谷歌通过他们的搜索引擎搜索任何特定演员的培根号码。

#### Kevin Bacon game

Upon the arrival of the 4G mobile network in the United Kingdom, Kevin Bacon appears in several commercials for the EE Network in which he links himself to several well known celebrities and TV shows in the UK.

The game "Six Degrees of Kevin Bacon"[22] was invented as a play on the concept: the goal is to link any actor to Kevin Bacon through no more than six connections, where two actors are connected if they have appeared in a movie or commercial together. It was created by three students at Albright College in Pennsylvania,[23] who came up with the concept while watching Footloose. On September 13, 2012, Google made it possible to search for any given actor's 'Bacon Number' through their search engine.[24]

Upon the arrival of the 4G mobile network in the United Kingdom, Kevin Bacon appears in several commercials for the EE Network in which he links himself to several well known celebrities and TV shows in the UK.

An early version involved former world Heavyweight boxing champion, John L. Sullivan, in which people would ask others to "shake the hand that shook the hand that shook the hand that shook the hand of 'the great John L.'"

#### John L. Sullivan

An early version involved former world Heavyweight boxing champion, John L. Sullivan, in which people would ask others to "shake the hand that shook the hand that shook the hand that shook the hand of 'the great John L.'"[25]

### In popular culture

#### Films

• The Oscar-winning film Babel is based on the concept of Six Degrees of Separation. The lives of all of the characters were intimately intertwined, although they did not know each other and lived thousands of miles from each other.

#### Games

• One of the achievements in the video game Brütal Legend is called "Six Degrees of Schafer," after the concept and Tim Schafer, who was presumably in the handful of players to have the achievement as of the game's release. A player can only obtain this achievement by playing online with someone who already has it, further paralleling it to the concept.
• One of the merits in the video game Torn City is called “domino.” The merit requires you to attack a person online who already has the merit.

#### Music

• The No Doubt song "Full Circle" has a central theme dealing with six degrees of separation.
• English progressive rock band Arena released an album titled The Seventh Degree of Separation in 2011.

< ! -- 请不要在列表中增加更多的例子! ! ！我只有一个例子来说明这一点

#### Television

• Six Degrees is a 2006 television series on ABC in the US. The show details the experiences of six New Yorkers who go about their lives without realizing they are affecting each other, and gradually meet one another.[26]

• Connected: The Power of Six Degrees is a 2008 television episode on the Science Channel in the US and abroad.[27]
• Lonely Planet Six Degrees is a TV travel show that uses the "six degrees of separation" concept: the hosts, Asha Gill and Toby Amies, explore various cities through its people, by following certain personalities of the city around and being introduced by them to other personalities.
• The television program Lost explores the idea of six degrees of separation, as almost all the characters have randomly met each other before the crash or someone the other characters know.
• The Woestijnvis production Man Bijt Hond, broadcast on Flemish TV, features a weekly section Dossier Costers, in which a worldwide event from the past week is linked to Gustaaf Costers, an ordinary Flemish citizen, in six steps.[28]
• The Israeli TV program Cultural Attache, presented by Dov Alfon, is based on the concept of Six Degrees of Separation. The first guest is asked to name a cultural figure with which he has an unexpected connection, and this person is interviewed and gives yet another name as connection, till the 6th person on the show, who is then asked about a possible connection to the first guest. Such connection is found in about 50% of the interviews.[29]
• Jorden rundt på seks steg is an ongoing Norwegian TV-series produced by NRK. In each episode, a pair of Norwegian celebrities are placed in one of the world's most remote areas and from there, asked to get in touch with a certain celebrity through a chain of six people. They are usually successful: In Season 1, three out of six pairs managed to get to their chosen celebrity in six steps; two of the pairs managed it in seven, and one pair managed it in five. In Season 2, all six pairs reached their target in six steps. https://tv.nrk.no/serie/jorden-rundt-paa-seks-steg

In 2013, Hungarian physicist Albert-László Barabási discovered that, on average, there are 19 degrees of separation between any two web pages.

2013年，匈牙利物理学家 albert-lászló Barabási 发现，任何两个网页之间平均有19度的分离度。

### Website and application

#### Internet

In 2013, Hungarian physicist Albert-László Barabási discovered that, on average, there are 19 degrees of separation between any two web pages.[31]

In late February 2018, the website www.SixDegreesOfWikipedia.com was published by Jacob Wenger. This site takes any two Wikipedia articles and finds the various hyperlink paths that interconnect the two in the fewest clicks. It then shows each of the steps that were taken to do so and also presents a graphical display of the connections. On March 14, 2018, the site stated that among searches up to that date (~half a million), there have been an average separation of 3.0190°. From these, the number of searches that required six or more degrees was 1.417 percent. It also stated that searches with no connection found was 1.07%, and this was attributed to certain articles being dead ends or having very few links. (Wenger's open source code is available on GitHub, and this enabled other sites to copy the concept, such as degreesofwikipedia.com.)

2018年2月下旬，雅各布 · 温格发布了一个网站，名为《 https://www.sixdegreesofwikipedia.com sixdegreesofwikipedia.com。这个网站只需要两篇维基百科文章，就可以找到不同的超链接路径，以最少的点击量将两者连接起来。然后，它显示了为此所采取的每个步骤，并且还显示了连接的图形显示。2018年3月14日，该网站表示，在截至当时的搜索中(约50万次) ，平均间隔为3.0190 ° 。其中，需要6个或更多学位的搜索次数为1.417% 。它还指出，没有发现连接的搜索占1.07% ，这是由于某些文章是死胡同或只有很少的链接。(Wenger 的开源代码可以在 GitHub 上找到，这使得其他网站可以复制这个概念，比如 http://degreesofwikipedia.com/ degreesofwikipedia.com。)

#### Six Degrees of Wikipedia

In late February 2018, the website www.SixDegreesOfWikipedia.com was published by Jacob Wenger. This site takes any two Wikipedia articles and finds the various hyperlink paths that interconnect the two in the fewest clicks. It then shows each of the steps that were taken to do so and also presents a graphical display of the connections. On March 14, 2018, the site stated that among searches up to that date (~half a million), there have been an average separation of 3.0190°. From these, the number of searches that required six or more degrees was 1.417 percent. It also stated that searches with no connection found was 1.07%, and this was attributed to certain articles being dead ends or having very few links.[32] (Wenger's open source code is available on GitHub, and this enabled other sites to copy the concept, such as degreesofwikipedia.com.)

A Facebook platform application named "Six Degrees" was developed by Karl Bunyan, which calculates the degrees of separation between people. It had over 5.8 million users, as seen from the group's page. The average separation for all users of the application is 5.73 degrees, whereas the maximum degree of separation is 12. The application has a "Search for Connections" window to input any name of a Facebook user, to which it then shows the chain of connections. In June 2009, Bunyan shut down the application, presumably due to issues with Facebook's caching policy; specifically, the policy prohibited the storing of friend lists for more than 24 hours, which would have made the application inaccurate. A new version of the application became available at Six Degrees after Karl Bunyan gave permission to a group of developers led by Todd Chaffee to re-develop the application based on Facebook's revised policy on caching data.

The initial version of the application was built at a Facebook Developers Garage London hackathon with Mark Zuckerberg in attendance.

A Facebook platform application named "Six Degrees" was developed by Karl Bunyan, which calculates the degrees of separation between people. It had over 5.8 million users, as seen from the group's page. The average separation for all users of the application is 5.73 degrees, whereas the maximum degree of separation is 12. The application has a "Search for Connections" window to input any name of a Facebook user, to which it then shows the chain of connections. In June 2009, Bunyan shut down the application, presumably due to issues with Facebook's caching policy; specifically, the policy prohibited the storing of friend lists for more than 24 hours, which would have made the application inaccurate.[33] A new version of the application became available at Six Degrees after Karl Bunyan gave permission to a group of developers led by Todd Chaffee to re-develop the application based on Facebook's revised policy on caching data.[34][35]

Yahoo! Research Small World Experiment has been conducting an experiment and everyone with a Facebook account can take part in it. According to the research page, this research has the potential of resolving the still unresolved theory of six degrees of separation.

The initial version of the application was built at a Facebook Developers Garage London hackathon with Mark Zuckerberg in attendance.[36]

Facebook's data team released two papers in November 2011 which document that amongst all Facebook users at the time of research (721 million users with 69 billion friendship links) there is an average distance of 4.74. It was also found that 99.91% of Facebook users were interconnected, forming a large connected component.

Yahoo! Research Small World Experiment has been conducting an experiment and everyone with a Facebook account can take part in it. According to the research page, this research has the potential of resolving the still unresolved theory of six degrees of separation.[22][37]

{ | class = “ wikitable infobox” Facebook's data team released two papers in November 2011 which document that amongst all Facebook users at the time of research (721 million users with 69 billion friendship links) there is an average distance of 4.74.[38][39] Probabilistic algorithms were applied on statistical metadata to verify the accuracy of the measurements.[40] It was also found that 99.91% of Facebook users were interconnected, forming a large connected component.[41]
Year Distance 距离
 Year Distance 2008 2008 2011 2011 2008 模板:Bartable 2016 2016 2011 模板:Bartable Distances as reported in Feb 2016 rises as reported in Feb 2016 2016 模板:Bartable

|-

Facebook reported that the distance had decreased to 4.57 in February 2016, when it had 1.6 billion users (about 22% of the world population).

| colspan="3"|Distances as reported in Feb 2016 [39][42]

|}

Facebook reported that the distance had decreased to 4.57 in February 2016, when it had 1.6 billion users (about 22% of the world population).[39]

The LinkedIn professional networking site operates the degree of separation one is away from a person with which he or she wishes to communicate. On LinkedIn, one's network is made up of 1st-degree, 2nd-degree, and 3rd-degree connections and fellow members of LinkedIn Groups. In addition, LinkedIn notifies the user how many connections they and any other user have in common.

The LinkedIn professional networking site operates the degree of separation one is away from a person with which he or she wishes to communicate. On LinkedIn, one's network is made up of 1st-degree, 2nd-degree, and 3rd-degree connections and fellow members of LinkedIn Groups. In addition, LinkedIn notifies the user how many connections they and any other user have in common.

SixDegrees.com was an early social-networking website that existed from 1997 to 2001. It allowed users to list friends, family members and acquaintances, send messages and post bulletin board items to people in their first, second, and third degrees, and see their connection to any other user on the site. At its height, it had 3,500,000 fully registered members. However, it was closed in 2000.

SixDegrees.com 是一个早期的社交网站，从1997年到2001年一直存在。它允许用户列出朋友、家庭成员和熟人，发送消息和贴布告栏的项目给他们的第一个、第二个和第三个学位的人，并查看他们与网站上任何其他用户的联系。在其鼎盛时期，它有350万正式注册会员。然而，它在2000年关闭了。

#### SixDegrees.com

SixDegrees.com was an early social-networking website that existed from 1997 to 2001. It allowed users to list friends, family members and acquaintances, send messages and post bulletin board items to people in their first, second, and third degrees, and see their connection to any other user on the site. At its height, it had 3,500,000 fully registered members.[43] However, it was closed in 2000.

Users on Twitter can follow other users creating a network. According to a study of 5.2 billion such relationships by social media monitoring firm Sysomos, the average distance on Twitter is 4.67. On average, about 50% of people on Twitter are only four steps away from each other, while nearly everyone is five steps or less away.

In another work, researchers have shown that the average distance of 1,500 random users in Twitter is 3.435. They calculated the distance between each pair of users using all the active users in Twitter.

Users on Twitter can follow other users creating a network. According to a study of 5.2 billion such relationships by social media monitoring firm Sysomos, the average distance on Twitter is 4.67. On average, about 50% of people on Twitter are only four steps away from each other, while nearly everyone is five steps or less away.[45]

Mathematicians use an analogous notion of collaboration distance: two persons are linked if they are coauthors of an article. The collaboration distance with mathematician Paul Erdős is called the Erdős number. Erdős-Bacon numbers and Erdős-Bacon-Sabbath (EBS) numbers are further extensions of the same thinking.

In another work, researchers have shown that the average distance of 1,500 random users in Twitter is 3.435. They calculated the distance between each pair of users using all the active users in Twitter.[46]

Watts and Strogatz showed that the average path length between two nodes in a random network is equal to , where = total nodes and = acquaintances per node. Thus if

Watts 和 Strogatz 证明了随机网络中两个节点之间的平均路径长度等于，其中 = 节点总数和每个节点的熟人数。因此，如果

## Mathematics

```= 300,000,000 (90% of the US population) and  = 30 then Degrees of Separation = 19.5 / 3.4 = 5.7 and if  = 6,000,000,000 (90% of the World population) and  = 30 then Degrees of Separation = 22.5 / 3.4 = 6.6.
```

= 300,000,000(美国人口的90%)和 = 30分离度 = 19.5/3.4 = 5.7，如果 = 6,000,000,000(世界人口的90%)和 = 30分离度 = 22.5/3.4 = 6.6。

Mathematicians use an analogous notion of collaboration distance:[47] two persons are linked if they are coauthors of an article. The collaboration distance with mathematician Paul Erdős is called the Erdős number. Erdős-Bacon numbers and Erdős-Bacon-Sabbath (EBS) numbers[48] are further extensions of the same thinking.

(Assume 10% of population is too young to participate.)

(假设10% 的人口年龄太小不能参与。)

Watts and Strogatz showed that the average path length between two nodes in a random network is equal to ln N / ln K, where N = total nodes and K = acquaintances per node. Thus if

N = 300,000,000 (90% of the US population) and K = 30 then Degrees of Separation = 19.5 / 3.4 = 5.7 and if N = 6,000,000,000 (90% of the World population) and K = 30 then Degrees of Separation = 22.5 / 3.4 = 6.6.

A 2007 article published in The Industrial-Organizational Psychologist, by Jesse S. Michel from Michigan State University, applied Stanley Milgram's small world phenomenon (i.e., “small world problem”) to the field of I-O psychology through co-author publication linkages. Following six criteria, Scott Highhouse (Bowling Green State University professor and fellow of the Society of Industrial and Organizational Psychology) was chosen as the target. Co-author publication linkages were determined for (1) top authors within the I-O community, (2) quasi-random faculty members of highly productive I-O programs in North America, and (3) publication trends of the target. Results suggest that the small world phenomenon is alive and well with mean linkages of 3.00 to top authors, mean linkages of 2.50 to quasi-random faculty members, and a relatively broad and non-repetitive set of co-author linkages for the target. The author then provided a series of implications and suggestions for future research.

2007年，密歇根州立大学的 Jesse s. Michel 在《工业-组织心理学家》上发表了一篇文章，将 Stanley Milgram 的小世界现象(即“小世界问题”)通过与合著者的联系应用到 I-O 心理学领域。根据6个标准，Scott Highhouse (鲍林格林州立大学教授，工业与组织心理学学会研究员)被选为目标。共同作者出版物的联系被确定为(1)在 I-O 社区的顶级作者，(2)准随机教师成员的高产 I-O 项目在北美，和(3)出版趋势的目标。研究结果表明，小世界现象仍然存在，平均作者联系数为3.00，平均作者联系数为2.50，与准随机教师成员的联系数为2.50。最后，作者对未来的研究提出了一系列的启示和建议。

(Assume 10% of population is too young to participate.)

## Psychology

A 2007 article published in The Industrial-Organizational Psychologist,[49] by Jesse S. Michel from Michigan State University, applied Stanley Milgram's small world phenomenon (i.e., “small world problem”) to the field of I-O psychology through co-author publication linkages. Following six criteria, Scott Highhouse (Bowling Green State University professor and fellow of the Society of Industrial and Organizational Psychology) was chosen as the target. Co-author publication linkages were determined for (1) top authors within the I-O community, (2) quasi-random faculty members of highly productive I-O programs in North America, and (3) publication trends of the target. Results suggest that the small world phenomenon is alive and well with mean linkages of 3.00 to top authors, mean linkages of 2.50 to quasi-random faculty members, and a relatively broad and non-repetitive set of co-author linkages for the target. The author then provided a series of implications and suggestions for future research.

## Notes

1. "More than half of all participants resided in North America and were middle class, professional, college educated, and Christian, reflecting commonly held notions of the Internet-using population"[11]
2. "suggesting lack of interest ... was the main reason" for the "extremely low completion rate"[11]

## References

1. Newman, Mark, Albert-László Barabási, and Duncan J. Watts. 2006. The Structure and Dynamics of Networks. Princeton, NJ: Princeton University Press.
2. Karinthy, Frigyes. (1929) "Chain Links."
3. Karinthy, Frigyes. Chain-Links. Translated from Hungarian and annotated by Adam Makkai and Enikö Jankó.
4. Gurevich, M (1961) The Social Structure of Acquaintanceship Networks, Cambridge, MA: MIT Press
5. de Sola Pool, Ithiel, Kochen, Manfred (1978–1979)."Contacts and influence." Social Networks 1(1): 42
6. de Sola Pool, Ithiel, Kochen, Manfred (1978–1979)."Contacts and Influence." Social Networks 1(1): 5–51
7. Milgram, Stanley (1967). "The Small World Problem". Psychology Today. 2: 60–67.
8. Travers, Jeffrey, and Stanley Milgram, "An Experimental Study of the Small World Problem", Sociometry 32(4, Dec. 1969):425–443
9. "The concept of Six degrees of separation stretches back to Italian inventor Guglielmo Marconi". Retrieved 16 July 2012.
10. Dodds, Muhamad, Watts (2003)."Small World Project," Science Magazine. pp.827-829, 8 August 2003 https://www.sciencemag.org/content/301/5634/827
11. Judith S. Kleinfeld, University of Alaska Fairbanks (January–February 2002). "The Small World Problem" (PDF). Society (Springer), Social Science and Public Policy.
12. Steven Strogatz, Duncan J. Watts and Albert-László Barabási "explaining synchronicity, network theory, adaption of complex systems, Six Degrees, Small world phenomenon in the BBC Documentary". BBC. Retrieved 11 June 2012. "Unfolding the science behind the idea of six degrees of separation"
13. BBC News: More Or Less: Connecting With People In Six Steps 13 July 2006, "Judith Kleinfeld ... told us, that 95% of the letters sent out had failed to reach the target."
14. "Six Degrees: Urban Myth? Replicating the small world of Stanley Milgram. Can you reach anyone through a chain of six people". Psychology Today. March 1, 2002.
15. The Uncontacted Indians of Brazil Survivalinternational
16. Duncan J Watts, Steven H Strogatz (1998). "Collective dynamics of 'small-world' networks". Nature. 393 (6684): 440–442. Bibcode:1998Natur.393..440W. doi:10.1038/30918. PMID 9623998. Unknown parameter `|s2cid=` ignored (help)
17. Jure Leskovec and Eric Horvitz (June 2007). "Planetary-Scale Views on an Instant-Messaging Network". arXiv:0803.0939. Bibcode:2008arXiv0803.0939L. Cite journal requires `|journal=` (help)
18. Robin Good. "The Power Of Open Participatory Media And Why Mass Media Must Be Abandoned". Robin Good's Master New Media.
19. Reza Bakhshandeh, Mehdi Samadi, Zohreh Azimifar, Jonathan Schaeffer, "Degrees of Separation in Social Networks", Fourth Annual Symposium on Combinatorial Search, 2011
20. Memorable quotes from Six Degrees of Separation. Accessed Nov. 11, 2006 from IMDB.com.
21. "Six degrees of separation' theory tested on Facebook". Telegraph. 17 August 2011. Retrieved 7 May 2012.
22. "Actor's Hollywood career spawned 'Six Degrees of Kevin Bacon'". Telegraph. 6 June 2011. Retrieved 7 May 2012.
24. Ecksel, Robert (1 January 2005). "The Great John L. Sullivan". The Sweet Science. IBofP. Retrieved 5 October 2019.
25. "Connected: The Power of Six Degrees". The Science Channel – Discovery Channel.
26. Het Nieuwsblad, 25 September 2009 "Archived copy". Archived from the original on 2011-05-01. Retrieved 2010-02-25.CS1 maint: archived copy as title (link)"Archived copy". Archived from the original on 2011-05-01. Retrieved 2010-02-25.CS1 maint: archived copy as title (link) (Dutch)
27. Israel's Channel 2 website [1] (Hebrew)
28. staff (July 13, 2015). "SIX DEGREES OF EVERYTHING (TRUTV) Premieres Tuesday, August 18". Futon Critic. Retrieved August 12, 2015.
29. /any two web pages are separated by just 19 clicks study finds
30. Insights On Hitler And More From The First 500,000 Searches by Jacob Wenger, March 14, 2018 (Searches with the same start and end page were not included in this average, and neither were articles in which no connection was found.)
31. "Six Degrees: come in, your time is up". K! - the blog of Karl Bunyan.
33. "Facebook Removing 24 Hour Caching Policy on User Data for Developers". insidefacebook.com.
34. "Archived copy". Archived from the original on 2012-07-07. Retrieved 2010-09-11.CS1 maint: archived copy as title (link)
35. "Archived copy". Archived from the original on 2011-09-26. Retrieved 2011-09-27.CS1 maint: archived copy as title (link)
36. Barnett, Emma (22 November 2011). "Facebook cuts six degrees of separation to four". Telegraph. Retrieved 7 May 2012.
37. "Three and a half degrees of separation – Facebook Research". Retrieved 9 July 2017.
38. Backstrom, Lars; Boldi, Paolo; Rosa, Marco; Ugander, Johan; Vigna, Sebastiano (2011-11-19). "Four Degrees of Separation". arXiv:1111.4570 [cs.SI].
39. Ugander, Johan; Karrer, Brian; Backstrom, Lars; Marlow, Cameron (2011). "The Anatomy of the Facebook Social Graph". arXiv:1111.4503 [cs.SI].
40. "Facebook says there are only 3.57 degrees of separation". Retrieved 4 February 2016.
41. Kirkpatrick, David (2010). The Facebook Effect: The Inside Story of the Company That Is Connecting the World. Simon & Schuster. ISBN 978-1439102121.
42. boyd, d. m; Ellison, N. B (2007). "Social network sites: Definition, history, and scholarship". Computer-Mediated. 13 (1): 210–230. doi:10.1111/j.1083-6101.2007.00393.x.
43. Apr 30, 2010, Six Degrees of Separation, Twitter Style, from Sysomos.
44. Reza Bakhshandeh, Mehdi Samadi, Zohreh Azimifar, Jonathan Schaeffer Degrees of Separation in Social Networks. Fourth Annual Symposium on Combinatorial Search, 2011
45. "MR: Collaboration Distance". ams.org.
46. "EBS Project". erdosbaconsabbath.com. Archived from the original on 2017-07-24.
47. (Michel, 2007)