# GraphCalc
[](https://graphcalc.readthedocs.io/en/latest/?badge=latest)
[](https://pypi.org/project/graphcalc/)
[](https://opensource.org/licenses/MIT)
[](https://doi.org/10.5281/zenodo.16907645)
[](https://doi.org/10.21105/joss.08383)
## Overview
`GraphCalc` is a Python library for computing a broad range of graph-theoretic invariants, purpose-built to support research in combinatorics, network science, and automated reasoning. It offers exact implementations of over 100 functions, spanning classical invariants (e.g., independence number, chromatic number, spectral radius) and a wide array of lesser-known parameters central to contemporary graph theory.
Originally developed as the invariant engine for the automated conjecturing system TxGraffiti, `GraphCalc` has since matured into a general-purpose research tool that facilitates the large-scale construction of structured, high-resolution invariant datasets. These datasets, often organized into tabular “knowledge tables,” form the basis for symbolic pattern mining, hypothesis generation, and downstream machine reasoning. For example,
```python
>>> import graphcalc as gc
>>> from graphcalc.polytopes.generators import cube_graph, octahedron_graph
>>> graphs = [cube_graph(), octahedron_graph()]
>>> functions = ["order", "size", "spectral_radius", "independence_number"]
>>> gc.compute_knowledge_table(functions, graphs)
order size spectral_radius independence_number
0 8 12 3.0 4
1 6 12 4.0 2
```
## 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
```
## Linear and Integer Programming Solvers
Many of the NP-hard graph invariant computations of GraphCalc depend on third-party solvers.At least one of the following is required if you intend to use solver-based functions (e.g., `gc.maximum_independent_set(G)`):
- **CBC** (recommended):
```bash
brew install cbc # macOS
sudo apt install coinor-cbc # Debian/Ubuntu
```
GraphCalc will attempt to automatically detect the solver if it is installed. You can also manually specify the solver in API calls.
## 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_knowledge_table(function_names, graphs)
```
## 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
Email: <rrd6@rice.edu>
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"description": "# GraphCalc\n\n[](https://graphcalc.readthedocs.io/en/latest/?badge=latest)\n[](https://pypi.org/project/graphcalc/)\n[](https://opensource.org/licenses/MIT)\n[](https://doi.org/10.5281/zenodo.16907645)\n[](https://doi.org/10.21105/joss.08383)\n\n\n## Overview\n\n`GraphCalc` is a Python library for computing a broad range of graph-theoretic invariants, purpose-built to support research in combinatorics, network science, and automated reasoning. It offers exact implementations of over 100 functions, spanning classical invariants (e.g., independence number, chromatic number, spectral radius) and a wide array of lesser-known parameters central to contemporary graph theory.\n\nOriginally developed as the invariant engine for the automated conjecturing system TxGraffiti, `GraphCalc` has since matured into a general-purpose research tool that facilitates the large-scale construction of structured, high-resolution invariant datasets. These datasets, often organized into tabular \u201cknowledge tables,\u201d form the basis for symbolic pattern mining, hypothesis generation, and downstream machine reasoning. For example,\n\n```python\n>>> import graphcalc as gc\n>>> from graphcalc.polytopes.generators import cube_graph, octahedron_graph\n>>> graphs = [cube_graph(), octahedron_graph()]\n>>> functions = [\"order\", \"size\", \"spectral_radius\", \"independence_number\"]\n>>> gc.compute_knowledge_table(functions, graphs)\n order size spectral_radius independence_number\n0 8 12 3.0 4\n1 6 12 4.0 2\n```\n\n## Features\n\n- **Maximum Clique**: Finds the maximum clique in a given graph.\n- **Chromatic Number**: Computes the minimum number of colors required for graph coloring.\n- **Vertex and Edge Cover**: Determines vertex and edge covers.\n- **Matching and Independence**: Calculates maximum matching and independent sets.\n- **Domination Number and its Variants**: Calculates the domination number, total domination number, and many other domination variants.\n- **Degree Sequence Invariants**: Calculates the residue, annihilaiton number, the slater number and more!\n- **Zero Forcing**: Calculates the zero forcing number, the total zero forcing number, the positive semidefinite zero forcing number, and the power domination number.\n\n## Installation\n\nTo install `graphcalc`, make sure you have Python 3.7 or higher, then install it:\n\n```bash\npip install graphcalc\n```\n\n## Linear and Integer Programming Solvers\n\nMany of the NP-hard graph invariant computations of GraphCalc depend on third-party solvers.At least one of the following is required if you intend to use solver-based functions (e.g., `gc.maximum_independent_set(G)`):\n\n- **CBC** (recommended):\n\n```bash\nbrew install cbc # macOS\nsudo apt install coinor-cbc # Debian/Ubuntu\n```\n\nGraphCalc will attempt to automatically detect the solver if it is installed. You can also manually specify the solver in API calls.\n\n## Example Graph Usage\n\n```python\nfrom graphcalc import (\n independence_number,\n domination_number,\n zero_forcing_number,\n)\nfrom graphcalc.generators import petersen_graph\n\n# Calculate and print the independence number of the Petersen graph.\nG = petersen_graph()\nprint(f\"Petersen graph independence number = {independence_number(G)}\")\n\n# Calculate and print the domination number of the Petersen graph.\nprint(f\"Petersen graph domination number = {domination_number(G)}\")\n\n# Calculate and print the zero forcing number of the Petersen graph.\nprint(f\"Petersen graph zero forcing number = {zero_forcing_number(G)}\")\n```\n\n## Example Polytope Usage\n\n```python\nimport graphcalc as gc\nfrom graphcalc.polytopes.generators import (\n cube_graph,\n octahedron_graph,\n dodecahedron_graph,\n tetrahedron_graph,\n icosahedron_graph,\n convex_polytopes_text_example,\n)\n\n# Generate polytope graphs (cubes, octahedra, etc.)\nG1 = cube_graph()\nG2 = octahedron_graph()\nG3 = dodecahedron_graph()\nG4 = tetrahedron_graph()\nG5 = icosahedron_graph()\nG6 = convex_polytopes_text_example(1)\nG7 = convex_polytopes_text_example(2)\n\n\n# Function names to compute\nfunction_names = [\n \"order\", # number of vertices\n \"size\", # number of edges\n \"p_vector\",\n \"independence_number\",\n \"vertex_cover_number\",\n \"maximum_degree\",\n \"average_degree\",\n \"minimum_degree\",\n \"spectral_radius\",\n \"diameter\",\n \"radius\",\n \"girth\",\n \"algebraic_connectivity\",\n \"largest_laplacian_eigenvalue\",\n \"second_largest_adjacency_eigenvalue\",\n \"smallest_adjacency_eigenvalue\",\n \"fullerene\",\n ]\n\n# Compute properties for multiple polytopes\ngraphs = [G1, G2, G3, G4, G5, G6, G7]\ndf = gc.compute_knowledge_table(function_names, graphs)\n```\n\n## Creating Simple Graphs, Polytope Graphs, and Simple Polytope Graphs\n\n```python\nimport graphcalc as gc\n\n# Draw a simple graph\nG = gc.SimpleGraph(name=\"Example Graph\")\nG.add_edges_from([(0, 1), (1, 2), (2, 3)])\nG.draw()\n```\n\n### Author\n\nRandy Davila, PhD\nEmail: <rrd6@rice.edu>\n",
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