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There are two extreme forms of network. One is laid out in an established pattern, like the wiring diagram*1 of a computer or the structure of an army. Such networks are totally ordered, like the regularly positioned atoms in a crystal lattice*2 or the precise patterning of a spider's web.

The other extreme form of network is one in which the links are formed at random.Random networks are a mathematician's joy. One of the most famous findings in the mathematics of networks is that if you keep adding random links to a network with only a few links, there comes a point when suddenly the whole network is interconnected. For example, if you have a group of people who mostly don't know each other, it is impossible to get a rumor spreading within the group. If all those in the group know and talk to just one other person, though, a rumor can spread very quickly. This is because the point at which interconnectedness suddenly occurs is when there is an average of exactly one link per node.*3

Random networks may be a mathematician's joy, but there are few real-world examples. One is the highway system; cities are the nodes, and highways are the links. One might also think that a random network of disease begins when someone sneezes*4 in public and passes the disease on to a group of strangers, who in turn pass it on to other strangers through their own sneezing. In practice, though, the resulting network of infection is far from random.

Most networks in real life are somewhere in between completely ordered and totally random. It was the idea of a totally random network, though, that inspired psychologist Stanley Milgram's famous small world experiments, which involved trying to send a letter to a perfect stranger. He wanted to know how many links there might be in a chain of connectedness between two random strangers.

In (1)his best-known experiment, Milgram asked a random group of 196 people in Nebraska*5 and 100 people in Boston*6 to try to get a letter to a man in Boston by sending the letter to someone they knew by their first name and who might be closer to that man, with a request to send it on to someone that they knew by their first name and who might be even closer, and so on.

Sixty-four chains reached their target, with an average number of just 5.5 steps for those starting in Nebraska and 4.4 for those starting in Boston. Milgram's experiment provided the inspiration for John Guare's 1990 play Six Degrees of Separation, which explores the idea that we are“bound to everyone on this planet by a trail link that's a thousand billion six people”. The play's title became a popular phrase, and, since then, many plays. books, films, and TV shows have been based on the same theme.

The simple statistics of a random network provide (2)a rational reason for why short chains of connection might be the standard case. Let's suppose that each of us knows 100 people fairly well, and that each of them knows 100 people fairly well. So in just two links, any of them will be connected to every other one of them. That's 10,000 people within just two links of each other. If each of them knows 100 people, that's 100×10,000=1 million people within three links of each other. Keep carrying the argument forward, and by the time you get to the sixth on people, which is considerably larger than our estimated world population of around 7 billion.

Other networks have similarly short chains, although the numbers are slightly different. The Web*7 for example, has nineteen degrees of separation, which means that any website*8 is an average of nineteen clicks from any other. (3)This may seem like a lot, but it's a small number compared to the over billion pages now on offer. If the links between pages were random, no figure could be accounted for by an average of just three links per website, since one billion is approximately equal to 3.

The six degrees experiment and the analysis of the Web demonstrate the reality of the small world theory, although neither case is an example of a totally random network. Still, it is fascinating, both socially and mathematically, to think that we are connected to any other person in the world by only six links.

【Adapted from The Perfect Swarm: The Science of Complexity in Everyday Life, by Len Fisher, Paperback ed. (2011) Basic Books, New York, pp. 108-111】

〔注〕
*1 wiring diagram:配線図
*2 crystal lattice:結品格子（結品の基本構造）
*3 node:連結点
*4 sneeze:くしゃみをする
*5 Nebraska:ネブラスカ（米国中部の州）
*6 Boston:ボストン（米国束部マサチューセッツ州の州都）
*7 Web:World Wide Webの略
*8 website:インターネット上のウェブサイト, ホームページ
〔設問〕

1. 下線部(1)の実験内容と結果を、本文の内容に沿って日本語で説明しなさい。
2. 下線部(2)が指すことを、本文の内容に沿って日本語で書きなさい。
3. 下線部(3)で述べられていることを、日本語で分かりやすく説明しなさい。
4. 本文の内容に関する次の文(1)~(5)を読み、正しいものには○、間違っているものには×を、それぞれ記入しなさい。
   • (1) A rumor will not spread in a group of people unless each one speaks to at least one other.
   • (2) The spreading of a disease is a good real-world example of an extreme form of random network.
   • (3) In Milgram's experiment, allot the letters reached their target ill less than 6 steps.
   • (4) Milgram's experiment was inspired by a play that was based on a popular phrase.
   • (5) According to the author, websites are an example of a completely random network.