LECTURE NOTES On NETWORK THEORY (BEES2211) 3rd Semester ETC Engineering Prepared by, Manjushree Jena Jemimah Digal Monalisha Nayak INDIRA GANDHI INSTITUTE OF TECHNOLOGY, SARANG
NETWORK THEORY Ms. Manjushree Jena Dept:-Electronics and Telecommunication
NETWORK TOPOLOGY 1. Introduction: When all the elements in a network are replaces by lines with circles or dots at both ends, configuration is called the graph of the network. A. Terminology used in network graph:(i) Path:- A sequence of branches traversed in going from one node to another is called a path. (ii) Node:- A node point is defined as an end point of a line segment and exits at the junction between two branches or at the end of an isolated branch. (iii) Degree of a node:- It is the no. of branches incident to it. 2-degree (iv) (v) (vi) (vii) (viii) (ix) (x) (xi) (xii) (xiii) 3-degree Tree:- It is an interconnected open set of branches which include all the nodes of the given graph. In a tree of the graph there can‟t be any closed loop. Tree branch(Twig):- It is the branch of a tree. It is also named as twig. Tree link(or chord):- It is the branch of a graph that does not belong to the particular tree. Loop:- This is the closed contour selected in a graph. Cut-Set:- It is that set of elements or branches of a graph that separated two parts of a network. If any branch of the cut-set is not removed, the network remains connected. The term cut-set is derived from the property designated by the way by which the network can be divided in to two parts. Tie-Set:- It is a unique set with respect to a given tree at a connected graph containing on chord and all of the free branches contained in the free path formed between two vertices of the chord. Network variables:- A network consists of passive elements as well as sources of energy . In order to find out the response of the network the through current and voltages across each branch of the network are to be obtained. Directed(or Oriented) graph:- A graph is said to be directed (or oriented ) when all the nodes and branches are numbered or direction assigned to the branches by arrow. Sub graph:- A graph said to be sub-graph of a graph G if every node of is a node of G and every branch of is also a branch of G. Connected Graph:- When at least one path along branches between every pair of a graph exits , it is called a connected graph.