cycless

A collection of algorithms to analyze a graph as a set of cycles.

Some codes come from https://github.com/vitroid/Polyhed and https://github.com/vitroid/countrings are integrated and improved.

API

API manual is here.

cycles.py

A simple algorithm to enumerate all irreducible cycles of n-members and smaller in an undirected graph. [Matsumoto 2007]

import cycless.cycles as cy
import networkx as nx

g = nx.cubical_graph()

for cycle in cy.cycles_iter(g, maxsize=6):
    print(cycle)

dicycles.py

An algorithm to enumerate the directed cycles of a size in a dircted graph. [Matsumoto 2021]

from genice2.genice import GenIce
from genice2.plugin import Lattice, Format, Molecule
import cycless.dicycles as dc

# Generate an ice I structure as a directed graph
lattice = Lattice("1h")
formatter = Format("raw", stage=(3,))
raw = GenIce(lattice, signature="ice 1h", rep=[2, 2, 2]).generate_ice(formatter)

for cycle in dc.dicycles_iter(raw["digraph"], size=6):
    print(cycle)

polyhed.py

An algorithm to enumerate the quasi-polyhedral hull made of cycles in an undirected graph. A quasi-polyhedral hull (vitrite) obeys the following conditions: [Matsumoto 2007]

1. The surface of the hull is made of irreducible cycles.
2. Two or three cycles shares a vertex of the hull.
3. Two cycles shares an edge of the hull.
4. Its Euler index (F-E+V) is two.

import cycless.cycles as cy
import cycless.polyhed as ph
import networkx as nx

g = nx.dodecahedral_graph()

cycles = [cycle for cycle in cy.cycles_iter(g, maxsize=6)]
for polyhed in ph.polyhedra_iter(cycles):
    print(polyhed)

simplex.py

Enumerate triangle, tetrahedral, and octahedral subgraphs found in the given graph.

References

1. M. Matsumoto, A. Baba, and I. Ohmine, Topological building blocks of hydrogen bond network in water, J. Chem. Phys. 127, 134504 (2007). http://doi.org/10.1063/1.2772627
2. Matsumoto, M., Yagasaki, T. & Tanaka, H. On the anomalous homogeneity of hydrogen-disordered ice and its origin. J. Chem. Phys. 155, 164502 (2021). https://doi.org/10.1063/5.0065215