Slide 1

Graph : Graph is a interconnection of all elements of the network ,by replacing all elements with a line segmentRank : The rank of a graph is N-1

Sub graph : Any subset of elements of the graph is called a sub graph. A sub graph is said to be proper if it is consists of strictly less than all the elements and nodes of the graphPath : A path is defined as a sub graph of connected elements such that not more than two elements are connected to any one node.

Tree :A Tree is an oriented connected sub graph of an graph containing all the nodes of the graph,but containing no loops .A tree has N-1 branches.The branches of a tree are called twigs and remaining branches of the graph are called links/chords

Co Tree : The links forms a sub graph .Co Tree is the complement of tree .There is a co-tree for every treeb = n-1No of links ,l=e-b l = e-n+1

Incidence Matrices

Element node Incidence matrix Bus incidence matrixBranch path Incidence matrixBasic cut set Incidence matrixAugmented cutest Incidence matrixBasic loop Incidence matrixAugment loop Incidence matrix

Augmented cut-set Incidence matrix (B)In the Basic cutest Incidence matrix ,the no of cutsets equal to the no of branches,The no of cutsets can be made equal to the no of elements by introducing fictitious or imaginary cutsets called Tie-cuts.Each Tie cut set contains only one link of the connected graph

Augmented loop incidence matrix

The utility of these augmented incidence matrices will be seen when non singular transformation method of obtaining network matrices