grcirc

C:\Users\emsorens\cernbox\Documents\grcirc-toolbox\grcirc\release

grcirc is a lightweight MATLAB toolbox for graph-theoretic analysis of linear DC circuits using Modified Nodal Analysis (MNA).

The toolbox combines classical circuit theory with graph topology tools such as incidence matrices, reduced incidence matrices, and fundamental cycle bases.

It is designed for:

• Control and electrical engineering students
• Circuit theory courses
• Graph theory applications in networks
• Rapid prototyping of DC networks
• Educational visualization of KCL and KVL

Features

DC Solver (MNA)

Solve linear DC circuits with:

• Resistors (R)
• Independent current sources (I)
• Independent voltage sources (V)

out = grcirc.solveDC(elems, "nNodes", N, "ground", g);

Returns:

• Node voltages
• Branch voltages
• Branch currents
• MNA system matrices
• KCL residual check

Graph-Theoretic Tools

• Full node–branch incidence matrix
• Reduced incidence matrix
• Fundamental cycle basis
• KCL verification
• KVL verification
• Connectivity checks (floating subcircuit detection)

Graph Visualization

grcirc.plotGraph(elems)

grcirc.plotGraph(elems, "directed", true)

Features:

• Automatic layout
• Directed/undirected graph mode
• Clean white background
• Automatic edge labels (type + value)
• Node labeling
• Compatible with custom coordinates

Element Model

Each branch is defined as:

elems(k).type % 'R', 'I', or 'V'

elems(k).n1 % start node

elems(k).n2 % end node

elems(k).value % element value

elems(k).name % optional label

Branch orientation is n1 → n2.

Example

elems = [

struct("type","R","n1",1,"n2",2,"value",10)

struct("type","V","n1",2,"n2",3,"value",5)

struct("type","R","n1",3,"n2",1,"value",5)

];

out = grcirc.solveDC(elems, "nNodes", 3, "ground", 3);

disp(out.v)

grcirc.plotGraph(elems, "directed", true)

Design Philosophy

• Sparse matrix formulation
• Graph-based formulation via incidence matrices
• Clean separation of topology and element physics
• Explicit KCL/KVL validation
• Educational clarity without sacrificing numerical rigor

Requirements

• MATLAB R2023b or newer (tested in R2025a)
• No external toolboxes required

Roadmap

Future releases may include:

• AC small-signal analysis
• Capacitors and inductors (s-domain)
• Controlled sources
• Multi-port network utilities
• Symbolic analysis mode