how do you find your dream job is obesity
contagious do you think a friends friend whom
you don't know has any influence at all in
your life and what has these questions to
do with let say how google works what are
the commonalities across these questions are
there any commonalities in the first place
well yes thats what makes the subject called
social networks so we will be studying all
these questions and more throughout the course
without any further ado let us start off with
a nice question so we are going to watch a
video clip right now i am going to come back
and then analyze what just happened in the
video clip
hey
hey ahmed where were you class is about to
start
leave it do you even know vardan and simran
are dating and for the heavens sake this is
just the second day of our college
how did you come to know about that
you don't know everyone knows about it
how is that even possible anamika told me
about it yesterday and that too personally
and i just told harita about it
harita who is harita i don't know her
as far as i know she does not talk to many
people here are it has been just one day since
we have met and i am still wondering how did
you come to know about that
of course not many of us know each other and
we have met each other yesterday only and
that too only few of us interacted
i see some signs going around here
let me revise it so we are the bunch of people
who haven't met each other before and then
met each other yesterday only and only few
of us interacted and still
and yet everyone knows about the news the
anamika told me personally
indeed only few of us know each other still
we are so connected
did you see what just happened in the video
clip there were these two friends who newly
joined this college and they are talking about
a piece of gossip and a person is asking this
question how come you know of this while i
thought nobody knows of this except me and
in fact that the person says the entire class
knows of this what is so intriguing about
this i actually find it intriguing for the
following reason
they are just less than one week into the
class in to the college and for everybody
to know this piece of gossip they all must
be friends with each other isn't it without
being friends with each other how who will
come and tell each other about all these things
they may not even be facebook friends this
early right it has been less than a week since
they have joined the college what is happening
here lets analyze
we need to develop a few pre requisites before
we can answer this question so let me go slowly
ok the classroom let say has some fifty people
fifty people may not be friends with each
other because as i told you it is just the
first few days of the class let me try modeling
this these are the fifty friends let me use
dots to denote these friends and the friendships
between them let me draw a line to denote
the friendship by this i mean assume rama
and krishna are part of this classroom and
they are friends with each other i put a line
between them and kirshna and ramesh are friends
with each other i put this line between them
and but rama and ramesh are not friends so
i don't put line between them and i develop
the friendship network i call this friendship
network
it might look something like this some points
denoting people and lines denoting friends
there are different hm ways in which people
call this dots are called vertices or nodes
in in the subject and the lines are called
edges or links so what we will be doing is
we will we are going to use the jargon vertices
or nodes for dots edges or links for lines
from now onwards throughout the course that's
with the nomenclature and now let medo a small
experiment and observe what is happening here
i will take fifty dots representing friends
ratherpeople in the class what i will do is
let me take a guess first week of theprogram
first week of the college and they are from
different places from the country and it has
only been first week so let say each person
would have managed to have three friends on
an average so what i will do is i will take
a person here and try to randomly pick three
people and declare him as friends with these
three people i do it for every single person
look at whats happening
the final graph i am going to call it as structure
a graph the final graph might look like this
what is surprising about this graph the surprising
fact is that while a person can actually make
all fifty people as his friends the entire
class as his friends forty nine to be precise
excluding him let say he just makes three
people as friends why because it's the beginning
of the course and what do i observe here in
this graph what is startling for me is that
this graph this network is connected what
do i mean by connected
you see take any two people here in this graph
there is a path that connects these two people
this is strange is this always true not really
observe the this particular example where
there are fifty people the twenty people this
side twenty five people that side they have
some friendships within but there is no friendships
across this might also happen in such a case
i don't call this graph connected
why because i can take a person from this
end and a person from that end there is not
path connecting these two people but then
look at my previous graph on an average if
i make three friends per person by picking
these three people uniformly at random i observe
that the graphs gets connected is this always
true
so let us look at this network twenty five
people this side twenty five people that side
as i told you and this side there is a network
of connections and that side there is a network
of connections remember here is a classroom
of fifty people and there is a bifurcation
of twenty five this side twenty five that
side
what do i mean by bifurcation i mean if you
look at the friendships between these people
twenty five peoplehave friendships within
them twenty five people have friendships within
them that side and a point to note is there
is no friendship across my question was is
this even possible so let me do one thing
i will now take a break write a piece of program
and get back to you people and tell you my
observationof course i will not show you the
program i will go do the program and came
back and tell you the output of the program
