SymmetricGraph

Some nice graph/group theory tools.

Two cabal projects are included: the tools themselves (CayleyOps) and output functions and executables (GraphOut). Also includes a Python file (compute_spectrum.py) for running eigenvalue algorithms on files composed of edge lists.

While there are executables included in the builds, I intended it mainly to be some study tools to be used from the GHCi REPL.

CayleyOps

This package is composed of the following modules:

• Cayley
  • Cayley.Algebra
  • Cayley.Matrix
  • Cayley.Graph
  • Cayley.Symmetric
  • Cayley.GraphAlg
  • Cayley.Examples

Cayley.Algebra

Abstract algebra types and manipulations. Supports finite groups and rings (over a numeric type) with fully-generic multiplications, specified by Cayley table.

Cayley.Matrix

Matrix operations pertinent to Graph theory, particularly direct sums, tensor products, and box products.

Cayley.Graph

Various graph manipulations based on Data.Graph. Includes adjacency matrix and edge list conversions, medial graphs, partitioning nodes by radii from a particular node, weak vs. strong regularity testing.

Cayley.Symmetric

Definitions and tools useful in building groups out of permutations, particularly symmetric group of a certain order.

Cayley.GraphAlg

Graph- and group-theoretical operations, like Cayley graph generation. Can also build probability (fusion?) algebras from graphs, where the elements of the algebra are steps on the graph of a particular size.

Cayley.Examples

Some example graph families and graphs. Includes complete graphs, paths, cycles, wheels, and skeleta of Platonic solids.

GraphOut

This package is composed of the following modules:

• Cayley.SymOut
• PythonNX

Cayley.SymOut

Various file-writing capabilities for both edge lists and adjacency matrices.

PythonNX

Tools for launching a Python REPL from Haskell. These scripts depend on NetworkX and compute_spectrum.py. Move the latter file around if it's not found by cabal repl.