So, let us look at what exactly happened,
we took Google sheets and tried seeing what
happens as we repeat this process alright.
What is the process?
Initially you give 1 by 3, 1 by 3 and 1 by
3 to all the notes correct you start with
the same values, it is the resources that
you have, we have used the example of gold
coins if you remember I repeat.
We have used the example of gold coins I am
saying resources, from now onwards I will
say just an assignment right it is the value
that I assigned and every time in every iteration
what you do is youthe value oflet us say A
is transferred to C, the value of C is transferred
to B the value of B is transferred equally
to A and C right we understand this so far
so good.
Now when I observed where it converges, we
observed that it indeed converges do you remember
the values, the values where 0.2, 0.4 and
0.4 you see that the total is equal to 1,
why is that?
That is very easy to see the resources that
you have distributed to these nodes do not
go out anywhere, they just remain in the network
itself.
This is like the law if you remember let me
write this down this is like the law of conservation
of energy correct, the law of conservation
of energy says energy can neither be created,
it cannot be created nor can it be destroyed.
What is happening here is exactly analogous
to the law of conservation of energy.
The sum total was one that is how you started
off with right and it remains 1 until the
end, but what just happened this process has
actually converged that is what you need to
understand.
How did it converge?
I suspect this was a coincidence that it converged.
It may not so happen for all the graph, will
it happen for any random graph?
If I take and then seeassign values to it
and I will observe that it converges, may
not be true.
Let us check for another graph to understand
this.
In this case the graph that I considered herelook
slightly trivial, by trivial I mean what is
it just 3 vertices and some 4 edges maybe
it looked very symmetric and that is why the
convergence happened.
Maybe it may not converge, just in case I
took some other graph; let us take some other
graph and then see whether it converges or
not.
