Signal flow graph, describing a RC circuit?

[dominicfhk]

Signal flow graph, describing a RC circuit?

Hi, guys. This is my first post on this forum!
I'm trying to understand this example in my textbook.

The current and voltage equations are:

where G=1/R, Z(s)=1/Cs, and I1(s)=I1
Then the text says the following signal flow graph can be obtained:

And finally we can somehow obtain the transfer function:

First question, why is it necessary to do the substitution for G, Z(s) and I1?
For the fourth equation, it says V3=I2Z, where Z(s)=1/Cs. Therefore, V3=I2/Cs (voltage=current/capacitance)? Where does this relationship comes from?
Lastly, how do I know how many equations do I need? And which circuit elements should I describe?

I might have more questions later, but I couldn't proceed without know the basics.
Thank you so much!

 

[lazyaditya]

V3 = I2Z , where Z(s) = 1/Cs this is because voltage across capacitance is given as CdV/dt=I thus taking laplace transform on both the sides we get sC*V(s)=I(s)
and V(s)=I(s)/sC therefore V3=I2/Cs.