Cycles

This notebook illustrates the search for cycles in graphs.

[1]:

from IPython.display import SVG

[2]:

import numpy as np

[3]:

from sknetwork.data import house, star, linear_digraph, cyclic_digraph
from sknetwork.topology import is_acyclic
from sknetwork.visualization import svg_graph

Graphs

[4]:

# star
graph = star(5, metadata=True)
adjacency = graph.adjacency
position = graph.position

[5]:

image = svg_graph(adjacency, position, scale=0.5)
SVG(image)

[5]:

../../_images/tutorials_topology_cycles_7_0.svg

[6]:

is_acyclic(adjacency)

[6]:

True

[7]:

# house graph
graph = house(metadata=True)
adjacency = graph.adjacency
position = graph.position

[8]:

image = svg_graph(adjacency, position, scale=0.5)
SVG(image)

[8]:

../../_images/tutorials_topology_cycles_10_0.svg

[9]:

is_acyclic(adjacency)

[9]:

False

Directed graphs

[10]:

# line
graph = linear_digraph(3, metadata=True)
adjacency = graph.adjacency
position = graph.position

[11]:

image = svg_graph(adjacency, position, scale=0.5)
SVG(image)

[11]:

../../_images/tutorials_topology_cycles_14_0.svg

[12]:

is_acyclic(adjacency)

[12]:

True

[13]:

# cycle
graph = cyclic_digraph(5, metadata=True)
adjacency = graph.adjacency
position = graph.position

[14]:

image = svg_graph(adjacency, position, scale=0.5)
SVG(image)

[14]:

../../_images/tutorials_topology_cycles_17_0.svg

[15]:

is_acyclic(adjacency)

[15]:

False