Graph theory of network elements

Introduction of Graph theory 

Today we study a circuit graph theory which is the part of circuit theory, In this theory we learn how to implement the basic concept of graph theory in circuit design.

The graph theory is simplify a circuit, In all circuit element (Resistance, capacitor or inductor ) are reduce by node ,dots and lines. The elements are represented One node to another node. The nodes are connected to line between two nodes. The all nodes are intersection of two or more branches and representing the network element of lines, voltage and current sources by their internal impedance. The line connected two or more points are called a node. And drawn lines are called branch. Number of branches is equal to the number of nodes. Node are denoted by small letters ( a, b, c ......) and Number (1, 2 ,3....) denoted to elements or branch.

Branch- 

A line which is connected to two and more than nodes this line are called branch. It is not shown which type of element is connected to the circuit. Only represent indirect or direct/oriented graph network path. In graph network min two branches and max two or more than branches.

Node- 

A point which is defined a first point or end point of element this point are called node. Nodes are isolated elements or branches. There are exactly two paths between ant pair of nodes in a circuit. Degree of a node is the number of branches incident to it.

Tree- 

It is connected to open set of branches. Tree is defined and distinct branch set in the close loop graph. Open set branches are interconnected to each other in this condition graph cannot be any close loop.

Tree branch or twig- 

Any branch of tree (n-1) is called a twig.

Chord - 

It is simplify the graph. It cannot be belong to any particular tree also called co-tree. Its linked to tree.

Path – 

An ordered sequence of branches way to one node to another node is called path in a graph.  

Properties of tree in a graph network theory

1.      Tree consists of nodes in a tree one path between two nodes.

2.      At least one tree is connected every graph.

3.      If the graph has N number of node, the tree will have (N-1) branches.

4.      Tree is open set of graph no closed path in the tree.

5.      Graph is depending on the number of nodes and branches.

Relation between Twigs and links

 The number of twigs on a tree is always one less than the no. of nodes (N-1).

N-No of Nodes

(N-1)- No of twigs

L= It represents the total no. of links.

B=Total no of branches

L=B-(N-1)

L=B-N+1

Circuit or loop-

In a graph tree contains a closed path this resultant is called loop or circuit.

Cut - set- 

The cut-set is separates part of elements or branches and dividing part are connected with dashed line. It separates the nodes into two groups. Cut sets containing only one twig are independent. T he number of cut sets is equal to the number of twigs.