DirectedGraph¶

class
menpo.shape.
DirectedGraph
(adjacency_matrix, copy=True, skip_checks=False)[source]¶ Bases:
Graph
Class for Directed Graph definition and manipulation.
Parameters:  adjacency_matrix (
(n_vertices, n_vertices, )
ndarray or csr_matrix) – The adjacency matrix of the graph in which the rows represent source vertices and columns represent destination vertices. The nonedges must be represented with zeros and the edges can have a weight value.  copy (bool, optional) – If
False
, theadjacency_matrix
will not be copied on assignment.  skip_checks (bool, optional) – If
True
, no checks will be performed.
Raises: ValueError
– adjacency_matrix must be either a numpy.ndarray or a scipy.sparse.csr_matrix.ValueError
– Graph must have at least two vertices.ValueError
– adjacency_matrix must be square (n_vertices, n_vertices, ), ({adjacency_matrix.shape[0]}, {adjacency_matrix.shape[1]}) given instead.
Examples
The following directed graph
>0<     1<>2   v v 3>4  v 5
can be defined as
import numpy as np adjacency_matrix = np.array([[0, 0, 0, 0, 0, 0], [1, 0, 1, 1, 0, 0], [1, 1, 0, 0, 1, 0], [0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0]]) graph = DirectedGraph(adjacency_matrix)
or
from scipy.sparse import csr_matrix adjacency_matrix = csr_matrix(([1] * 8, ([1, 2, 1, 2, 1, 2, 3, 3], [0, 0, 2, 1, 3, 4, 4, 5])), shape=(6, 6)) graph = DirectedGraph(adjacency_matrix)
The following graph with isolated vertices
0<   1 2  v 3>4 5
can be defined as
import numpy as np adjacency_matrix = np.array([[0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 1, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0]]) graph = DirectedGraph(adjacency_matrix)
or
from scipy.sparse import csr_matrix adjacency_matrix = csr_matrix(([1] * 3, ([2, 2, 3], [0, 4, 4])), shape=(6, 6)) graph = DirectedGraph(adjacency_matrix)

children
(vertex, skip_checks=False)[source]¶ Returns the children of the selected vertex.
Parameters:  vertex (int) – The selected vertex.
 skip_checks (bool, optional) – If
False
, the given vertex will be checked.
Returns: children (list) – The list of children.
Raises: ValueError
– The vertex must be between 0 and {n_vertices1}.

find_all_paths
(start, end, path=[])¶ Returns a list of lists with all the paths (without cycles) found from start vertex to end vertex.
Parameters:  start (int) – The vertex from which the paths start.
 end (int) – The vertex from which the paths end.
 path (list, optional) – An existing path to append to.
Returns: paths (list of list) – The list containing all the paths from start to end.

find_all_shortest_paths
(algorithm='auto', unweighted=False)¶ Returns the distances and predecessors arrays of the graph’s shortest paths.
Parameters:  algorithm ('str', see below, optional) –
The algorithm to be used. Possible options are:
‘dijkstra’ Dijkstra’s algorithm with Fibonacci heaps ‘bellmanford’ BellmanFord algorithm ‘johnson’ Johnson’s algorithm ‘floydwarshall’ FloydWarshall algorithm ‘auto’ Select the best among the above  unweighted (bool, optional) – If
True
, then find unweighted distances. That is, rather than finding the path between each vertex such that the sum of weights is minimized, find the path such that the number of edges is minimized.
Returns:  distances (
(n_vertices, n_vertices,)
ndarray) – The matrix of distances between all graph vertices.distances[i,j]
gives the shortest distance from vertexi
to vertexj
along the graph.  predecessors (
(n_vertices, n_vertices,)
ndarray) – The matrix of predecessors, which can be used to reconstruct the shortest paths. Each entrypredecessors[i, j]
gives the index of the previous vertex in the path from vertexi
to vertexj
. If no path exists between verticesi
andj
, thenpredecessors[i, j] = 9999
.
 algorithm ('str', see below, optional) –

find_path
(start, end, method='bfs', skip_checks=False)¶ Returns a list with the first path (without cycles) found from the
start
vertex to theend
vertex. It can employ either depthfirst search or breadthfirst search.Parameters:  start (int) – The vertex from which the path starts.
 end (int) – The vertex to which the path ends.
 method ({
bfs
,dfs
}, optional) – The method to be used.  skip_checks (bool, optional) – If
True
, then input arguments won’t pass through checks. Useful for efficiency.
Returns: path (list) – The path’s vertices.
Raises: ValueError
– Method must be either bfs or dfs.

find_shortest_path
(start, end, algorithm='auto', unweighted=False, skip_checks=False)¶ Returns a list with the shortest path (without cycles) found from
start
vertex toend
vertex.Parameters:  start (int) – The vertex from which the path starts.
 end (int) – The vertex to which the path ends.
 algorithm ('str', see below, optional) –
The algorithm to be used. Possible options are:
‘dijkstra’ Dijkstra’s algorithm with Fibonacci heaps ‘bellmanford’ BellmanFord algorithm ‘johnson’ Johnson’s algorithm ‘floydwarshall’ FloydWarshall algorithm ‘auto’ Select the best among the above  unweighted (bool, optional) – If
True
, then find unweighted distances. That is, rather than finding the path such that the sum of weights is minimized, find the path such that the number of edges is minimized.  skip_checks (bool, optional) – If
True
, then input arguments won’t pass through checks. Useful for efficiency.
Returns:  path (list) – The shortest path’s vertices, including
start
andend
. If there was not path connecting the vertices, then an empty list is returned.  distance (int or float) – The distance (cost) of the path from
start
toend
.

get_adjacency_list
()¶ Returns the adjacency list of the graph, i.e. a list of length
n_vertices
that for each vertex has a list of the vertex neighbours. If the graph is directed, the neighbours are children.Returns: adjacency_list (list of list of length n_vertices
) – The adjacency list of the graph.

has_cycles
()¶ Checks if the graph has at least one cycle.
Returns: has_cycles (bool) – True
if the graph has cycles.

has_isolated_vertices
()¶ Whether the graph has any isolated vertices, i.e. vertices with no edge connections.
Returns: has_isolated_vertices (bool) – True
if the graph has at least one isolated vertex.

init_from_edges
(edges, n_vertices, skip_checks=False)¶ Initialize graph from edges array.
Parameters:  edges (
(n_edges, 2, )
ndarray) – The ndarray of edges, i.e. all the pairs of vertices that are connected with an edge.  n_vertices (int) – The total number of vertices, assuming that the numbering of
vertices starts from
0
.edges
andn_vertices
can be defined in a way to set isolated vertices.  skip_checks (bool, optional) – If
True
, no checks will be performed.
Examples
The following undirected graph
0     12     34   5
can be defined as
from menpo.shape import UndirectedGraph import numpy as np edges = np.array([[0, 1], [1, 0], [0, 2], [2, 0], [1, 2], [2, 1], [1, 3], [3, 1], [2, 4], [4, 2], [3, 4], [4, 3], [3, 5], [5, 3]]) graph = UndirectedGraph.init_from_edges(edges, n_vertices=6)
The following directed graph
>0<     1<>2   v v 3>4  v 5
can be represented as
from menpo.shape import DirectedGraph import numpy as np edges = np.array([[1, 0], [2, 0], [1, 2], [2, 1], [1, 3], [2, 4], [3, 4], [3, 5]]) graph = DirectedGraph.init_from_edges(edges, n_vertices=6)
Finally, the following graph with isolated vertices
0   1 2   34 5
can be defined as
from menpo.shape import UndirectedGraph import numpy as np edges = np.array([[0, 2], [2, 0], [2, 4], [4, 2], [3, 4], [4, 3]]) graph = UndirectedGraph.init_from_edges(edges, n_vertices=6)
 edges (

is_edge
(vertex_1, vertex_2, skip_checks=False)¶ Whether there is an edge between the provided vertices.
Parameters:  vertex_1 (int) – The first selected vertex. Parent if the graph is directed.
 vertex_2 (int) – The second selected vertex. Child if the graph is directed.
 skip_checks (bool, optional) – If
False
, the given vertices will be checked.
Returns: is_edge (bool) –
True
if there is an edge connectingvertex_1
andvertex_2
.Raises: ValueError
– The vertex must be between 0 and {n_vertices1}.

is_tree
()¶ Checks if the graph is tree.
Returns: is_true (bool) – If the graph is a tree.

isolated_vertices
()¶ Returns the isolated vertices of the graph (if any), i.e. the vertices that have no edge connections.
Returns: isolated_vertices (list) – A list of the isolated vertices. If there aren’t any, it returns an empty list.

n_children
(vertex, skip_checks=False)[source]¶ Returns the number of children of the selected vertex.
Parameters: vertex (int) – The selected vertex. Returns:  n_children (int) – The number of children.
 skip_checks (bool, optional) – If
False
, the given vertex will be checked.
Raises: ValueError
– The vertex must be in the range[0, n_vertices  1]
.

n_parents
(vertex, skip_checks=False)[source]¶ Returns the number of parents of the selected vertex.
Parameters:  vertex (int) – The selected vertex.
 skip_checks (bool, optional) – If
False
, the given vertex will be checked.
Returns: n_parents (int) – The number of parents.
Raises: ValueError
– The vertex must be in the range[0, n_vertices  1]
.

n_paths
(start, end)¶ Returns the number of all the paths (without cycles) existing from start vertex to end vertex.
Parameters:  start (int) – The vertex from which the paths start.
 end (int) – The vertex from which the paths end.
Returns: paths (int) – The paths’ numbers.

parents
(vertex, skip_checks=False)[source]¶ Returns the parents of the selected vertex.
Parameters:  vertex (int) – The selected vertex.
 skip_checks (bool, optional) – If
False
, the given vertex will be checked.
Returns: parents (list) – The list of parents.
Raises: ValueError
– The vertex must be in the range[0, n_vertices  1]
.

n_edges
¶ Returns the number of edges.
Type: int

n_vertices
¶ Returns the number of vertices.
Type: int

vertices
¶ Returns the list of vertices.
Type: list
 adjacency_matrix (