Network Theory Lecture: Cut Set, Fundamental Cut Set, and Cut Set Matrix

Introduction

Definition: Removal of some branches from a graph to bisect it into two parts.
Characteristics:
- Removes branches; parts may not be equal or identical.
- Necessary to bisect the graph.
Example:
- Removing branches A, B, and C isolates Node 1 from another part of the graph.
- Removing branches A, E, and F isolates Node 3 from branches B, C, and D.

Definition: A cut set that includes one twig and the rest as links.
Relation to Tree: Identify a tree in the graph:
- The number of branches in the tree = Total nodes - 1.
- The tree should not form a closed loop.
- Example tree: B, E, D (without closed loop)
Components:
- Twigs: Branches included in the tree.
- Links: Branches not part of the tree.
Example Setup:
- Twigs: B, E, D
- Links: A, C, F
- Fundamental Cut Sets:
  - Cut Set 1 (C1): Twig B, Links A, C
  - Cut Set 2 (C2): Twig E, Links A, F
  - Cut Set 3 (C3): Twig D, Links C, F

Definition: Represents orientation of branches with respect to fundamental cut sets.
Orientation:
- Direction of cut set aligns with the direction of the twig in fundamental cut set.
Direction Rules:
- +1: Branch direction matches cut set direction.
- -1: Branch direction opposes cut set direction.
- 0: Branch not connected with cut set.
Example Construction:
- Cut Sets: C1, C2, C3
- Branches: A, B, C, D, E, F
- Example Matrix:
  - C1: A(-1), B(+1), C(-1), D(0), E(0), F(0)
  - C2: A(+1), B(0), C(0), D(0), E(+1), F(-1)
  - C3: A(0), B(0), C(-1), D(+1), E(0), F(-1)

These concepts are foundational to calculating the cut set matrix.
Next Steps:
- Explore properties of tie set matrix and cut set matrix.
- Formulate KCL and KVL equations based on these matrices.