GraphReveal

Have you ever needed an example of a graph that, e.g., is Hamiltonian, has exactly 8 vertices, and can be drawn on a plane without intersecting edges? Or wondered how many graphs of size 10 are bipartite, have no isolated vertices, and have exactly two components?

This package aims to answer some of your questions. You can search through all graphs with some reasonable order (currently 9 is the maximum) using a very simple DSL (domain-specific language).

Installation

Make sure that you have Python in a sufficiently recent version. To install the package using pip, you can use the following command:

pip install graphreveal

Basic usage

Firstly, you should create the database:

graphreveal create-database

This process should take less than a second and will create a database of graphs with order no greater than 7. To use a larger database, add the --n 8 or --n 9 flag to this command (it should take no more than a couple of minutes).

Some examples

graphreveal search "10 edges, bipartite, no isolated vertices, 2 components"

graphreveal count "5..6 vertices, connected"

graphreveal count "5 vertices, connected, not (eulerian | planar)"

Command search will print a list of graphs in graph6 format. You can use houseofgraphs.org to visualize them. Command count will simply output the number of specified graphs.

List of available properties

• [N] vertices (alternatives: verts,V, nodes)
• [N] edges (alternative: E)
• [N] blocks (alternative: biconnected components)
• [N] components (alternative: C)
• acyclic (alternative: forest)
• bipartite
• complete
• connected
• cubic (alternative: trivalent)
• eulerian (alternative: euler)
• hamiltonian (alternative: hamilton)
• no isolated vertices (alternatives: no isolated v, niv)
• planar
• regular
• tree

As [N], you can use a simple number or range (e.g., 3-4, 3..4, < 5, >= 2). You can also negate any property using ! or not. Use | for alternatives (disjunction) and parentheses () for grouping. Conjunction (, or ;) binds tighter than |.