Network Graphs#
Analyzing the structure of a lumped circuit is essential for finding all instances of Kirchhoff's laws within it. Mathematically, the structure is modelled using a directed multigraph which encodes how the electrical elements are connected with each other.
Algorithm: Network Graph Construction
Constructing the network graph of a lumped circuit is done in the following way:
- Construct the nodes
- Every distinct region of uninterrupted wire is represented by exactly one node.
- The ground (if any) is also represented by exactly one node.
- Construct the edges
- For a component with \(p\) terminals, identify the node to which each terminal is connected. Pick one of these nodes and create edges between it and the other \(p-1\) nodes.
- For a component with \(2p\) terminals which can be modelled as a \(p\)-port, draw an edge between the nodes to which the terminals of each port are connected.
- Choose a direction for each edge.