Interconnection of some elements is an electrical circuit. A circuit is a network. So to differentiate between a circuit and a network, we should understand the path of circuit.
A branch represents a single element such as voltage source or a current source or a resistor.
We can say that a branch is two terminals of an element. The circuit figure shows 5 branches in the circuit. There is two sources one 20V voltage source, one 4A current source, three resistors. As the circuit contains five elements so it has five branches. Every element has two terminals also.
A node is the point of connection between two or more branches.
Node is indicated by dot sign. When a short circuit has two nodes it actually becomes one node. If we redraw the first circuit as it has two common points shown in black color filled.
After redrawing the circuit becomes as below circuit. It shows three nodes a, b, c.
A loop is any closed path in a circuit.
Loop counts starting at a node passing through a set of nodes and returning to the starting node without passing through any node more than once.
A loop is said to be independent if it contains at least one branch which is not a part of any other independent loop. From independent path or independent loop we get independent set of the equations. We can consider above circuit to define set of loop. For 4Ω resistor consider with independent 20V voltage source there path abca is a loop. If we think second loop for 6Ω with independent 4A current source then we get another loop. Such way many set of loop can be made.
A network with b branches, n nodes and l independent loops will satisfy the fundamental theorem of network topology,
b = l + n – 1
Two or more elements are in series if they exclusively share a single node and consequently carry the same current.
Two or more elements are in parallel if they are connected to the same two nodes and consequently have the same voltage across them.
Question: Now tell how many branches and nodes are in below circuit?
Answer: the circuit has five branches as it contains five elements. It has three nodes. Because short path is counted one node.