How to study Network Analysis?
What I have observed during my preparation twice is that unnecessary information is provided in most of the coaching institute’s modules which is not at all important for GATE exam. Most of the topics in EC and EE curriculum for the Network Theory is same except the Three Phase Circuits, Graph Theory and Magnetic Circuits which are additional topics in EE curriculum. This post is very detailed and I hope through this post you get an idea on how to prepare Network Analysis.
Network Analysis is a problembased subject where mostly practicing the problems is much more important than reading the theory and hence for studying the concepts, any book can be followed such as Fundamentals of Electric Circuits by Alexander Sadiku or else you can download pdf notes from NPTEL. For solving problems you can refer Circuit Theory by A Chakraborathy and Previous Year GATE and ESE problems in both EE and ECE.
The following chapters are part of Network Theory:

Network Basics
This chapter is the foundation stone for Network Analysis and its roots are present in Electromagnetic Theory that we study in 10+2. The topics that need to be studied in this chapter are first of all the nature of circuit elements such as Linear and Nonlinear elements, Active and Passive Elements etc. and the basics of Resistance, Inductance and Capacitance such as Power, Energy, CurrentVoltage relationships etc. Then you need to study about equivalent impedance and the techniques such as Source Transformation etc. Then you have to attempt basic circuit solving using the techniques such as Nodal and Mesh Analysis as these methods are very powerful and will even help you in other subjects.
The basics of energy and power should also be studied which is very helpful in other EE core subjects so you need to understand how you can determine the direction of power flow i.e. power being absorbed or delivered.

Graph Theory
The questions from this topic in GATE are very rare but still, this topic should be prepared for the sake of completeness. Here small topics are very much important like the number of trees possible for a given network but the concepts like Incidence, CutSet and TieSet Matrix are not very much important but still should be once looked at as there is no harm. Also, different terminology should be remembered like twigs, links etc. This topic is not present in ECE GATE Curriculum.

Network Theorems
For GATE, the names of theorems are not very much important but for IES they can come in handy for Objective Paper. So, it is better to remember the name and usage of theorems and the most important theorems are Thevenin and Norton Theorem as sometimes the equivalent circuit can be directly asked, other than that theorems like Superposition, Tellegen’s theorem is not very important.
Here, StarDelta Transformation is important as it can be used with other subjects as like Electrical guys can use the same for Transient Stability Analysis for Fault away from line ends in Power Systems and Maximum Power Transfer Theorem is also important but there is one trick involved there as well that this theorem is only applicable when you need to derive the maximum power delivered to load and the load resistance is variable.

SteadyState Sinusoidal Analysis
The most important concept under this topic is the concept of Phasors which I believe comes more naturally for Electrical guys as they encounter Phasors more often in Electrical Machines and Power Systems. This is important as it reduces the effort immensely for solving an AC Network and also for this topic, you need to have a command on dealing with complex numbers by hand as complex functionality is not present in Virtual Calculator.
After that, you also need to study how the Network Theorems change for AC circuits as when there are multiple sources having different frequencies the Superposition Theorem comes in handy. The maximum power transfer theorem is a bit more complicated as compared to DC circuits as there are different cases based on Load and Source Impedance.
The concept of Resonance is also very important under this topic and the key to that is just to equate the imaginary part of Impedance and Admittance to zero based on the case under consideration. Also, you need to remember basic formulas for Quality factor and bandwidth for Series and Parallel RLC networks. Then you also need to have the basic knowledge about drawing the locus diagram of different phasor quantities in an AC network. This topic is small but sometimes asked and it is very much similar to Polar Plot in Control Systems so you can easily understand it by relating it to Polar Plot.

Transient Analysis
The transient response for general circuits like RC and RL circuits should be directly remembered in terms of initial and final conditions as that will save you a lot of time and can be used many places else like Chopper circuits in Power Electronics for EE Guys. Other than that there is not much but you should always try to solve one or two problems completely by forming the differential equations and solving them so that you can always handle the nonstandard cases.
Also, there are second order networks such as RLC network and LC oscillator and in those cases, you need to understand how to write the response based on whether the network is underdamped, critically damped or overdamped. LC oscillator comes in handy when we study about Power Electronics.

Circuit Analysis using Laplace Transform
This topic is important as this comes in handy even for Control Systems also and here the important thing to remember is to include the initial conditions in the models for Inductor and Capacitor in the sdomain and also you need to remember some common Laplace Transforms which you may do anyways in Signals and Systems. The circuits should be analyzed using Laplace Transform when the supply is not a constant voltage DC source or a step voltage source. in those cases, you can directly use the Transient Equation for Networks.

State Equations for Networks
This topic is covered in more detail in Control Systems. Here, you need to define state model for the Electrical Networks by suitably choosing the state variables. This topic is not included in GATE EE curriculum.

2Port Networks
Here the important parameters are Zparameters, Yparameters, Hparameters and Transmission Parameters and you need to memorize the conditions for Symmetry and Reciprocity in terms of various parameters. Also, one more thing is important here as to what parameters are added or multiplied for different network configurations like Cascaded Connection, Parallel Connection, and others. To find these parameters you just need to remember the Network Equations for various parameters and then decide which quantity should be equated to zero to find a particular parameter which avoids the need to memorize the formulas for these parameters.

Three Phase Circuits
Three Phase Circuits come more naturally to EE guys as they have to deal with threephase circuits in Electrical Machines and Power Systems, so in Network Theory only the basics of those are covered and the thing to be remembered is the relationships between Phase and Line quantities (Voltage and Current) for both Star and Delta Connections.
These relationships are very handy as they can be used directly for balanced 3phase circuits and unbalanced circuits will be solved completely stepbystep as there are no direct relations but the questions from this topic are very rare.

Magnetic Circuits
This topic though not directly mentioned under Network Analysis curriculum but it is present under EMT in GATE EE curriculum. The topics that you need to study in this chapter are basics of MMF, Flux, and Reluctance and these concepts will help you in Electrical machines. Other than that Dot Convention is very important for Transformers. If you have a grip on these concepts then you can compute Equivalent Inductance in circuits consisting of Magnetically Coupled Coils.
I hope you have got a fair idea of what to study and what not to study for GATE and in case you have queries regarding Network Analysis, feel free to comment.