Network
Science or the SmallWorld Phenomen
The 6 degrees of separation hypothesis
basically states that any 2 people on Earth
are connected by no more than six levels
of acquaintances. Even in the vast confusion
of the World Wide Web, on the average,
one page is only about 16 to 20 clicks
away from any other...
Strogatz and Watts offered a mathematical
explanation for the results of a landmark
experiment performed in the 1960s at Harvard
by social psychologist Stanley Milgram.
The researcher gave letters to randomly
chosen residents of Omaha and asked them
to deliver the letters to people in Massachusetts
by passing them from one person to another.
The average number of steps turned out
to be about six!
Following their experiment, Strogatz and
Watts created a mathematical model of a
network in which each point, or node, is
closely connected to many other nodes nearby.
When they added just a few random connections
('shortcuts') between a few widely separated
nodes, messages could travel from one node
to any other much faster than the size
of the network would suggest. The six degrees
of separation idea works, because in every
small group of friends there are a few
people who have wider connections, either
geographically or across social divisions.
Until recently, we assumed that it would
be our close relationships that would bring
us the information and opportunities we
have been looking for, but the science
of networking says different. It is our
bare acquaintances, our friends of acquaintances,
who can play crucial roles in our lives.
These kinds of relationships are called weak or loose
ties. The people we hang out with
don't often give us the breakthrough contacts
or information we want because, generally
speaking, we know the same people and the
same information that they know.
The 6 degrees of separation can be demonstrated
statistically. Assuming that a person only
knows 45 people, and each
of these know 45n nonredundant
people and so up to six degrees, this multiplies
out to be:
45
=
45 x 44 =
45 x 44 x 43 =
45 x 44 x 43 x 42 =
45 x 44 x 43 x 42 x 41 =
45 x 44 x 43 x 42 x 41 x 40 =

45
1,980
85,140
3,575,880
146,611,080
5,864,443,200

Total 
6,014,717,325 
Which
is enough to cover the world's population!
Here
is the math formula to calculate approximately
the degree of separation of any population:
d = log N / log k,
where N represents
the actual number of people; and k,
the average number of acquaintances per
person. Using the example above, we obtain:
d = log 6,014,717,325 / log 45
= 5.9... which can be rounded to 6!
The
smallworld phenomenon could provide
answers to a wide range of practical
questions, such as how ideas spread,
how fads catch on, how a small initial
failure can cascade throughout a large
power grid or financial system, and how
companies can foster internal networks
to cope with rapidly changing competitive
environments.
