An electric network consists of interconnected network elements. The connections are called nodes and the connecting elements between nodes form the branches of a network. The graph of a network shows the branches as lines and the nodes as dots. Below are a few definitions that we will use throughout this text:
A connected graph is a graph that has at least one path among the branches that connects all the nodes.
A sub-graph is a subset of branches with their corresponding nodes.
A closed path of branches is called a loop.
A collection of branches that isolates a sub-graph when removed is called a cut set.
A tree is a collection of branches that connects all the nodes but has no loops.