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Mark Buchanan, in his book, "Nexus: Small Worlds and the Groundbreaking Science of Networks", describes how mathematicians Duncan Watts & Steve Strogatz
 stumbled over their peculiar graph… that held the key to revealing how it is that six billion people can be connected by only six links.
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SMALL WORLDS: THE SCIENCE— HOW MANY HANDSHAKES DOES IT TAKE?
Sixty million handshakes:
In a perfectly ordered world, if you cast a huge fishnet around the world, until all six billion people are connected it would take sixty million connections or handshakes to make contact with someone halfway around the world.
Now, for every ten thousand people in that six billion, introduce just two additional random connections— or shortcuts— between any two people. Here is where the power of a small world gets spooky and the magic begins.
Eight handshakes:
With this addition of only two random shortcuts, per ten thousand people, it now takes only eight handshakes to meet someone halfway around the world. Not eight million— 8!
Five handshakes:
Add a third random shortcut, and the handshakes drop to five. You are just 5 handshakes away from anyone in the world.
Networking is:
Reaching out and shaking someone’s hand, engaging that person in conversation and connecting your networks. Imagine the possibilities!
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