The document discusses representing electrical circuits as graphs for computer simulation. It describes that a circuit can be expressed as a directed graph consisting of branches that connect at nodes. For large circuits, a computer program needs the circuit expressed as fundamental matrices including the node-incidence matrix, basic cutset matrix, and basic loop matrix. These matrices provide a standard form for the program to analyze the graph representation of the circuit.

1. 9 July 2014
Lecture 7,8

2. ECE203 - Network Analysis - K.Jeya Prakash - Kalasalingam University
Suppose we wish to find the node voltages of the circuit below.
We know how to do this by hand.
For large-scale circuits, we may wish to do this via a computer simulation
(i.e. PSpice). We will need to express this circuit in a standard form for
input to the program.

3. Consists of branches
and nodes
Describes
interconnection of
elements of a network
DiGraph (Directed
Graph) – Arrow indicate
directions of current
and voltages in a circuit
Directed Graph also
called Oriented graph
ECE203 - Network Analysis - K.Jeya Prakash - Kalasalingam University

4. Current direction – same as arrow direction
Voltage direction – arrow goes from + to –
through element
ECE203 - Network Analysis - K.Jeya Prakash - Kalasalingam University
+ V –
I

5. Branch: Line segment connecting a pair of nodes
in the graph of a network
Node: A terminal of a branch, which is
represented by a point (dot)
Degree of a node: The number of branches
incident at a node of a graph
A graph is connected if and only if there is a path
between every pair of nodes
A path is said to exist between any two nodes, if
it is possible to reach from one node to other
node
ECE203 - Network Analysis - K.Jeya Prakash - Kalasalingam University

6. A loop exists, if there is more than one
path between two nodes
A loop is a set of branches of a graph
forming a closed path
ECE203 - Network Analysis - K.Jeya Prakash - Kalasalingam University
For example:
•branches a, c, d
•branches a, b, e, c
Form a loop in the
graph

7. Planar graph: A graph which can be drawn on
a plane surface such that no two branches
cross each other
Non Planar: A graph which can not be drawn
of a plane surface such that no two branches
cross each other
ECE203 - Network Analysis - K.Jeya Prakash - Kalasalingam University

8. Tree: Connected subgraph of a network which consists of
all the nodes of the original graph but no closed paths
A tree is a set of branches of a graph which contains no
loop. Including one more branch to a tree will create a
loop
Thus tree is a maximal set of branches which will not have
a loop
Twigs: Branches of a tree
Co-tree: In forming a tree, certain branches are removed
or opened. They are called links or link branches. Set of all
links of a given tree is called a co-tree
ECE203 - Network Analysis - K.Jeya Prakash - Kalasalingam University

9. ECE203 - Network Analysis - K.Jeya Prakash - Kalasalingam University
— tree
…. co-tree

10. Number of nodes of a graph = Number of nodes
in a tree
Number of twigs – Tree value of graph or Rank of
the tree
ECE203 - Network Analysis - K.Jeya Prakash - Kalasalingam University
n = number of nodes
b = number of branches
t = number of tree branches
l = number of co-tree branches
t = n – 1
l = b – t = b – n + 1
t = n – 1
l = b – t = b – n + 1

11. There are three fundamental matrices
representing the graph of a given circuit:
Node-incidence matrix (A-matrix)
Basic cutset matrix (Q-matrix)
Basic loop matrix (B-matrix)
They are very useful in computer-aided
systematic analysis.
ECE203 - Network Analysis - K.Jeya Prakash - Kalasalingam University

12. ECE203 - Network Analysis - K.Jeya Prakash - Kalasalingam University