# Definitions Related To Graph Of A Network

**Loop : **It is the closed contour selected in the graph.

**
Cut-set :** It is that set of elements or branches of a graph that separates two main parts of a network. If any branch of the cut-set is not removed, the network remains connected.

**
Tree and Co-tree :** Tree is an interconnected open set of branches which include all the nodes of the given graph. In a tree of a graph there cannot be any closed loop. A branch of tree is known as

**twig**. Those branches of a graph which are not included a tree are called

**co-tree.**The branches of a co-tree are called

**links**or

**chords.**

Total no. of links L = B â€“ (N â€“ 1) = B â€“ N + 1

where B = total no. of branches

N = no. of Nodes

N â€“ 1 = total no. of tree branches

Number of independent KCL equations = N â€“ 1

**
Planar graph :** It is drawn on a two-dimensional plane so that no two branches intersect at a point which is not a node.

**Fig. : **Planar graph

**
Non-planar graph : **It is drawn on a two dimensional plane such that two or more branches intersect at a point other than node on a graph.

**Fig. :** Non-planar graph

Rank of a graph.

If there exists N number of nodes, then rank R of a graph is given by the relation

R = (N â€“ 1)

Reduced Incidence Matrix

When one row is removed from the complete incidence matrix, the remaining matrix is called reduced incidence matrix.

If [A] is the reduced incidence matrix and [A* ^{t}*] is the transposed matrix of [A] then, the number of possible trees of a graph

T = Determinant [A] [A* ^{t}*]

Fundamental Cut-Set

No. of fundamental cut-sets = no. of twigs = (N â€“ 1)

where N = no. of nodes of a graph

**Number of independent node equations (n) = J(no. of junctions) â€“ 1.**

**Number of independent mesh equations (m) = ***b*** (no. of branches) â€“ ( j â€“ 1)**