# GraphCalc
[](https://graphcalc.readthedocs.io/en/latest/?badge=latest)
## Overview
`graphcalc` is a Python package for performing a variety of graph computations, including maximum clique detection, chromatic number calculation, and vertex cover identification. It is built on top of `networkx` and provides efficient implementations of fundamental graph theory algorithms.
## Features
- **Maximum Clique**: Finds the maximum clique in a given graph.
- **Chromatic Number**: Computes the minimum number of colors required for graph coloring.
- **Vertex and Edge Cover**: Determines vertex and edge covers.
- **Matching and Independence**: Calculates maximum matching and independent sets.
- **Domination Number and its Variants**: Calculates the domination number, total domination number, and many other domination variants.
- **Degree Sequence Invariants**: Calculates the residue, annihilaiton number, the slater number and more!
- **Zero Forcing**: Calculates the zero forcing number, the total zero forcing number, the positive semidefinite zero forcing number, and the power domination number.
## Installation
To install `graphcalc`, make sure you have Python 3.7 or higher, then install it:
```bash
pip install graphcalc
```
## Example Graph Usage
```python
from graphcalc import (
independence_number,
domination_number,
zero_forcing_number,
)
from graphcalc.generators import petersen_graph
# Calculate and print the independence number of the Petersen graph.
G = petersen_graph()
print(f"Petersen graph independence number = {independence_number(G)}")
# Calculate and print the domination number of the Petersen graph.
print(f"Petersen graph domination number = {domination_number(G)}")
# Calculate and print the zero forcing number of the Petersen graph.
print(f"Petersen graph zero forcing number = {zero_forcing_number(G)}")
```
## Example Polytope Usage
```python
import graphcalc as gc
from graphcalc.polytopes.generators import (
cube_graph,
octahedron_graph,
dodecahedron_graph,
tetrahedron_graph,
icosahedron_graph,
convex_polytopes_text_example,
)
# Generate polytope graphs (cubes, octahedra, etc.)
G1 = cube_graph()
G2 = octahedron_graph()
G3 = dodecahedron_graph()
G4 = tetrahedron_graph()
G5 = icosahedron_graph()
G6 = convex_polytopes_text_example(1)
G7 = convex_polytopes_text_example(2)
# Function names to compute
function_names = [
"order", # number of vertices
"size", # number of edges
"p_vector",
"independence_number",
"vertex_cover_number",
"maximum_degree",
"average_degree",
"minimum_degree",
"spectral_radius",
"diameter",
"radius",
"girth",
"algebraic_connectivity",
"largest_laplacian_eigenvalue",
"second_largest_adjacency_eigenvalue",
"smallest_adjacency_eigenvalue",
"fullerene",
]
# Compute properties for multiple polytopes
graphs = [G1, G2, G3, G4, G5, G6, G7]
df = gc.compute_graph_properties_dataframe(function_names, graphs)
print(df)
```
## Creating Simple Graphs, Polytope Graphs, and Simple Polytope Graphs
```python
import graphcalc as gc
# Draw a simple graph
G = gc.SimpleGraph(name="Example Graph")
G.add_edges_from([(0, 1), (1, 2), (2, 3)])
G.draw()
```
### Author
Randy Davila, PhD
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