from small world network from the Santa Fe Institute Bulletin, Volume 14, Number 2 (Fall 1999).

I think this image illustrate the idea of different networks better than any graphs in the book. very well suited for the discussion in the book.

most real-world networks appear to fall somewhere in between the ordered and random extremes. Friendship networks are a good example of this in-between state. Since people meet most new friends through existing friends, the networks are locally ordered. (Here order means that if A knows B and B knows C, then A is more likely to know C than some other random element.) The outcome of local ordering in such a network is that one individual’s friends are more likely than not to know one another: a characteristic that is called “clustering.” Many real-world networks, including friendship networks, tend to be highly clustered, but they are not entirely so. If a person joins a club and meets new people or moves to a different city to take a job, new connections can form that are not ordered by the existing network.

- from small world network

The idea of clustering is the human instinct to form familiar circle with safety and intimacy. We are all related to familiar first degree friends in a close way; however, we are also related to the not so closed contacts through friends. Some stories always go: “my friend’s friend’s friend…” With a weak tie of your friend’s friend’s friend, your circle gets a little bit bigger because the parameter is widen. Each person is connected to at least first degree family and the first degree contacts around everyday life setting. Some clusters are tighter than others, but we can see all the clusters connected together. All the clusters connected together would make the world smaller because everything is connected. In a sense, the world becomes a wide-ranged cluster, it’s just not very tightly connect. (In another word, a lower clustering coefficient.) The idea of clustering actually can be found in nature too. It is the synchronization that we notice all the time. For example of the crickets that chirp at the same harmonized tone. This example in the book made me think about emergence. The crickets listen to each other very carefully and adjust their chirp to match the neighbors. It is the neighborhood interaction that creates the distributed chirping. If we see the crickets as nodes in a cluster, it would be one following another and becomes a bigger and bigger cluster. If we apply this to human in a society setting, it is actually true too; moreover, it illustrates the growth of clusters. People often meet new people through different people, and it may be human instinct, but other people would join in if you are meeting someone new. (or meeting someone new and then introduce to existing friends.) The cluster gets bigger then.
I see the work of networking and clustering right in the act of gossiping. People call it rumors because it spreads so fast and so wide no one can track it down to the source. People interact with each other and tell each other things. If 1 person tells 2 people…. (you can do the math). We can see how small the world is just by thinking how someone from the US know about “bad reputation of Surrey girl.” (I know it sounds like a joke but someone from US told me about the bad reputation of Surrey girl.) I don’t know how bad the reputation is of the Surrey girls, but I certainly know that it’s a small world because even people in the US knows a tiny town in Vancouver. However, this raises my question about whether when rumor itself becomes so well-known because of the power of networking, would it become a fact instead of a rumor? (This is under the consumption that rumors are not true.)

emergence six degrees theory