http://venus.ece.ndsu.nodak.edu/ece/academics/courses/ee206/notes/cirtop.htm

*: a representation of a circuit where each branch is denoted by a line segment.*

**Graph****: a set of branches (each denoted by a line segment) that connects every node to every other node via some path without forming a loop.**

*Tree*(of a graph)*: a branch of a graph that is part of a particular tree.*

**Tree branch***: those branches of a graph which are not part of a particular tree. This is also known as the*

**Cotree***complement of the tree*.

*: a branch of a cotree.*

**Link***: a minimum set of branches that, when cut, will divide a graph into two separate parts.*

**Cut set***: a cut set containing only a single tree branch.*

**Fundamental cut set***: A loop that results when a link is put into the tree.*

**Fundamental loop**
A

*cut set*divides a*graph*into two independent parts. In terms of the original circuit, a KCL equation can be written for either part of the circuit divided by the cut; such a KCL equation is called a*cut-set equation.*

*The dual of a*

*fundamental cut set*is a*fundamental loop*. Each time a*link*is inserted into a*tree*as a potential*tree branch*, a*loop*is formed in the*tree*(thus the resulting object is no longer a*tree*). Such a*loop*is called a*fundamental loop*.

**Tree-branch analysis**uses KCL (Kirchhoff's Current Law) but no reference node is selected like is done in nodal analysis; all KCL equations are written in terms of*tree branch*voltages instead of*node voltages*.

**Loop analysis**uses KVL (Kirchhoff's Voltage Law) but the loops chosen may not necessarily be meshes. Instead, each loop needs to be a*fundamental loop*obtained by inserting a*link*into a*tree*.

There is only one

*graph*for a circuit (although there may be many ways to draw it).
Usually, there are several

*trees*for a*graph*, and each*tree*has a corresponding*cotree*.
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