facebook:六度分离理论或将改写

1967年美国社会心理学家米尔格伦(Stanley Milgram)提出了一个“六度分离” 理论。简单地说,该理论认为在人际交往的脉络中,任意两个陌生人都可以通过“亲友的亲友”建立联系,这中间最多只要通过五个朋友就能达到目的(当时米尔格伦的研究是结论是 5.2 )。通俗点说:你和任何一个陌生人之间所间隔的人不会超过五个,也就是说,最多通过五个人你就能够认识任何一个陌生人。

可是,超过三十年来这个理论所谓的人际连系网(例如上述的“世界上所有人”)仍然有所争议。从论文发表至今有关这方面的研究很少。不过,在应用层面方面却很多,特别是保险及传销业的从业员。现时在香港,一般保险经纪在完成交易之后,都会要求客户提供一个至少五人的新名单。另外,早在1980年代初期,《读者文摘》就已利用这理论,鼓励订户向公司推荐其他潜在订户。

微软的研究人员Jure Leskovec 和 Eric Horvitz 过滤2006年某个单一月份的MSN短信,利用二点四亿使用者的三百亿通讯息进行比对,结果发现任何使用者只要透过平均6.6人就可以和全数据库的一千八百亿组配对产生关连。48%的使用者在6次以内可以产生关连,而高达78%的使用者在7次以内可以产生关连。

但世界世界比我们想象的更小。今天社交网络巨头 Facebook和米兰大学共同宣布了他们关于六度分离理论的新研究成果:他们已经确定世界上任何两个独立的人之间平均所间隔的人数为4.74。

Facebook 的此次研究是采用的米兰大学 Web 算法实验室(Laboratory for Web Algorithmics of the Università degli Studi di Milano)开发的 state-of-the-art 算法(state-of-the-art algorithms),研究表明,用六度来描述实际中两个人之间联系的间隔稍微显得有点大,实际在Facebook上, 任何2个用户之间只有5度间隔的概率是99.6%,任何2个用户之间只有 4 度间隔的概率是92%。

Facebook 的研究对象是一个月内访问 Facebook 的7.21亿活跃用户,超过世界人口的10%,所以他们的结论应该更加可信,如果研究成果可信的话,那么六度分离理论或将被改写。(Via Our4.org)

【文章全文一】Anatomy of Facebook

Think back to the last time you were in a crowded airport or bus terminal far from home. Did you consider that the person sitting next to you probably knew a friend of a friend of a friend of yours? In the 1960s, social psychologist Stanley Milgram’s “small world experiment” famously tested the idea that any two people in the world are separated by only a small number of intermediate connections, arguably the first experimental study to reveal the surprising structure of social networks.

With the rise of modern computing, social networks are now being mapped in digital form, giving researchers the ability to study them on a much grander, even global, scale. Continuing this tradition of social network research, Facebook, in collaboration with researchers at the Università degli Studi di Milano, is today releasing two studies of the Facebook social graph.

First, we measured how many friends people have, and found that this distribution differs significantly from previous studies of large-scale social networks. Second, we found that the degrees of separation between any two Facebook users is smaller than the commonly cited six degrees, and has been shrinking over the past three years as Facebook has grown. Finally, we observed that while the entire world is only a few degrees away, a user’s friends are most likely to be of a similar age and come from the same country.

In our studies, performed earlier this year, we examined all 721 million active Facebook users (more than 10% of the global population), with 69 billion friendships among them. To date, these are the largest social network studies ever released.

How many friends?

An important basic view of any social network is the cumulative degree distribution, which shows the percentage of individuals that have less than a given number of friends. As you can see above, only 10% of people have less than 10 friends, 20% have less than 25 friends, while 50% (the median) have over 100 friends. Meanwhile, because the distribution is highly skewed, the average friend count is 190. An important finding from our study, however, is that the distribution is not nearly as skewed as earlier studies of social networks have suggested.

At first glance, the median friend count on Facebook — 100 — may seem surprisingly low; a quick survey of my own friends reveals that they almost all have more than 100 friends. But no, your friends are not atypically social – a classic paradox regarding social networks dictates that, for most people, the median friend count of their friends is higher than their own friend count. On Facebook, that’s the case for 84% of our users. Why? Scott Feld wrote about this phenomenon in his 1991 paper Why Your Friends Have More Friends than You Do, showing that the same phenomenon dictates that college students typically find that their classes to be larger than the average class size, and that when sitting on an airplane, it will typically be more crowded than the average occupancy. These effects all arise because for people, classes, and flights to be popular, you must be much more likely to choose them. So you shouldn’t feel bad if it seems like all your friends are more popular than you: it appears this way to most of us.

Four degrees of separation.

The idea of ‘six degrees of separation’ -- that any two people are on average separated by no more than six intermediate connections -- was first proposed in 1929 in a short story by Hungarian author Frigyes Karinthy, and made popular by the John Guare play and movie, Six Degrees of Separation. The idea was first put to the test by Stanley Milgram in the 1960’s. Milgram selected 296 volunteers and asked them to dispatch a message to a specific individual, a stockholder living in the Boston suburb of Sharon, Massachusetts. The volunteers were told that they couldn’t send the message directly to the target person (unless the sender knew them personally), but that they should route the message to a personal acquaintance that was more likely than the sender to know the target person. Milgram found that the average number of intermediate persons in these chains was 5.2 (representing about 6 hops). The experiment showed that not only are there few degrees of separation between any two people, but that individuals can successfully navigate these short paths, even though they have no way of seeing the entire network.

While we will never know if it was true in 1929, the scale and international reach of Facebook allows us to finally perform this study on a global scale. Using state-of-the-art algorithms developed at the Laboratory for Web Algorithmics of the Università degli Studi di Milano, we were able to approximate the number of hops between all pairs of individuals on Facebook. We found that six degrees actually overstates the number of links between typical pairs of users: While 99.6% of all pairs of users are connected by paths with 5 degrees (6 hops), 92% are connected by only four degrees (5 hops). And as Facebook has grown over the years, representing an ever larger fraction of the global population, it has become steadily more connected. The average distance in 2008 was 5.28 hops, while now it is 4.74.

Thus, when considering even the most distant Facebook user in the Siberian tundra or the Peruvian rainforest, a friend of your friend probably knows a friend of their friend. When we limit our analysis to a single country, be it the US, Sweden, Italy, or any other, we find that the world gets even smaller, and most pairs of people are only separated by 3 degrees (4 hops). It is important to note that while Milgram was motivated by the same question (how many individuals separate any two people), these numbers are not directly comparable; his subjects only had limited knowledge of the social network, while we have a nearly complete representation of the entire thing. Our measurements essentially describe the shortest possible routes that his subjects could have found.

Your friends and you.

It’s easy for me to imagine that a path from me to a random person in Siberia goes first to one of my few Russian friends in California, and then hops around the globe to a friend of theirs living in Russia. But, while I can imagine these short paths connecting all pairs of people in the world, this notion stands in sharp contrast to my day-to-day experience. Most of my friends live in the US, and the ones I am closest to live within just a few miles of me.

This is what makes social networks somewhat unique: they are both well-connected in the sense that you can reach anyone from anyone else in a relatively short number of hops, but at the same time, they are very locally clustered, with the vast majority of connections spanning a short distance. In our study, we found that 84% of all connections are between users in the same country. But this isn’t the only dimension along which people tend to cluster. We also find that people tend to have a similar, albeit typically smaller, number of friends as their neighbors, and tend to be about the same age. Somewhat surprisingly, even for individuals aged 60, the distribution of their friends’ ages is sharply peaked at exactly 60.

Conclusions

To facilitate open access within the scientific community, the two works are available for download:

In these two works, we show how the Facebook social network is at once both global and local. It connects people who are far apart, but also has the dense local structure we see in small communities. We show that, as Facebook has grown over the years, representing an ever larger fraction of the global population, it has become even more connected. In the years to come, we look forward to continuing to illuminate social trends and helping people understand how the world is becoming more connected.
【文章出处】http://www.facebook.com/notes/fa ... k/10150388519243859

【文章全文二】Separating You and Me? 4.74 Degrees
The world is even smaller than you thought.

Cornell News Service/ Jon Kleinberg of Cornell said weak ties could be important.

Adding a new chapter to the research that cemented the phrase “six degrees of separation” into the language, scientists at Facebook and the University of Milan reported on Monday that the average number of acquaintances separating any two people in the world was not six but 4.74.

The original “six degrees” finding, published in 1967 by the psychologist Stanley Milgram, was drawn from 296 volunteers who were asked to send a message by postcard, through friends and then friends of friends, to a specific person in a Boston suburb.

The new research used a slightly bigger cohort: 721 million Facebook users, more than one-tenth of the world’s population. The findings were posted on Facebook’s site Monday night.

The experiment took one month. The researchers used a set of algorithms developed at the University of Milan to calculate the average distance between any two people by computing a vast number of sample paths among Facebook users. They found that the average number of links from one arbitrarily selected person to another was 4.74. In the United States, where more than half of people over 13 are on Facebook, it was just 4.37.

“When considering even the most distant Facebook user in the Siberian tundra or the Peruvian rain forest,” the company wrote on its blog, “a friend of your friend probably knows a friend of their friend.” The caveat there is “Facebook user” — like the Milgram study, the cohort was a self-selected group, in this case people with online access who use a particular Web site.

Though the study was by far the largest of its kind, it raised questions about definitions of terms like “friend” on Facebook.

A Microsoft study in 2008, using a more conservative definition of friend, found an average chain of 6.6 people in a group of 240 million who exchanged chat messages. Eric Horvitz, a Microsoft researcher who led the study in 2008, said that network was based on people who exchanged messages, rather than those who identified as “buddies.”

“There is an issue of how many friends you actually have,” he said. But, he said, the Internet might have altered the definition.

“My own notion of what a friend is has evolved,” he said.

Jon Kleinberg, a computer science professor at Cornell and a faculty adviser to an author of the new study, said some links might be more meaningful than others.

He offered the example of a man wanted for a crime. A random Facebook user might discover that she took a class with someone who rented an apartment from someone who grew up with the suspect. They may all be connected as Facebook “friends.”

“We are close, in a sense, to people who don’t necessarily like us, sympathize with us or have anything in common with us,” Dr. Kleinberg said. “It’s the weak ties that make the world small.”

Still, he noted that such ties were hardly meaningless. “We should ask what things spread well on weak ties,” he said. “News spreads well on weak ties. Those people I met on vacation, if they send me some cool news, I might send that to my friends. If they send me something about a protest movement, I might not.”

Matthew O. Jackson, an economist at Stanford who studies social networks, raised questions about the bias built into a study based on random samples. He said the study confirmed Facebook’s success in being where millions of people communicate. “It’s more evidence that they’ve been enormously successful at connecting a large number of people very well,” he said.

The research underscores the growing power of the emerging science of social networks, in which scientists study the ways people interact by crunching gigantic sets of Internet data.

“These social network tools provide individuals with tremendous reach,” said Dr. Horvitz, the Microsoft researcher. “People can share ideas with only a few jumps to a large portion of the world’s population and with even fewer steps to the entire population of a nation.”

In addition to social scientists, a new generation of Internet commerce is using social network research to market products, and Pentagon sleuths are using similar techniques to identify networks of insurgents.

The “six degrees” concept dates to a 1929 short story, “Chains,” in which Frigyes Karinthy, the Hungarian author, suggested that no one is more than a string of six friends away from any other person.

After Milgram published his famous paper “The Small World Problem,” in 1967, the playwright John Guare made “Six Degrees of Separation,” the title of a 1990 play that explored Milgram’s premise. And that gave rise to the parlor game Six Degrees of Kevin Bacon, in which disparate Hollywood personalities are linked to one another. (Elvis Presley was in “Change of Habit” with Edward Asner; Mr. Asner was in “J.F.K.” with Kevin Bacon.)

The Facebook paper, titled “Four Degrees of Separation,” notes that Milgram posed both an optimistic interpretation of his findings and a pessimistic one.

On one hand, it is a startling notion that reaching someone on the other side of the world takes only a small group of social connections. On the other hand, Milgram said, the result could also be evidence of psychological distance: that we were actually, on average, five “worlds apart.”

“From this gloomier perspective,” the new paper says, “it is reassuring to see that our findings show that people are in fact only four worlds apart, and not five.”

A version of this article appeared in print on November 22, 2011, on page B1 of the New York edition with the headline: Separating You and Me? 4.74 Degrees.

【文章作者】JOHN MARKOFF and SOMINI SENGUPTA

【文章来源】Published: November 21, 2011
read more at the new york times

 


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