There are 4 nodes in the network.

Loop Analysis:
A loop is a closed path in a network that does not contain any other closed paths within it. In this case, there are 3 independent loops in the network.

The number of branches in the network can be determined using the loop and node equations.

Loop Equation:
In loop analysis, we use Kirchhoff's voltage law (KVL) to write equations for each loop. The loop equation for each independent loop is given by:
Σ(Vi) = 0
where Vi is the voltage across each branch in the loop.

Node Equation:
In node analysis, we use Kirchhoff's current law (KCL) to write equations for each node. The node equation for each node is given by:
Σ(Ii) = 0
where Ii is the current entering or leaving the node.

Analysis:
Now let's analyze the given network.

Since there are 4 nodes, we can write 4 node equations. However, the number of unknown currents is equal to the number of branches minus one. Hence, we can write 3 node equations.

Since there are 3 independent loops, we can write 3 loop equations.

Now, the total number of equations we have is 3 (loop equations) + 3 (node equations) = 6.

The number of unknowns in the network is equal to the number of branches. Let's assume the number of branches is 'n'.

So, we have 'n' unknown currents and 'n' unknown voltages.

Since we have 'n' unknowns and 'n' equations, the system is solvable.

The number of branches in the network is equal to the number of unknowns, which is 'n'.

Therefore, the number of branches in the network is 6.

Hence, the correct answer is option D) 6.