"""
Operations on graphs including union, intersection, difference.
"""
import networkx as nx
__all__ = [
"union",
"compose",
"disjoint_union",
"intersection",
"difference",
"symmetric_difference",
"full_join",
]
[docs]def union(G, H, rename=(None, None), name=None):
""" Return the union of graphs G and H.
Graphs G and H must be disjoint, otherwise an exception is raised.
Parameters
----------
G,H : graph
A NetworkX graph
rename : bool , default=(None, None)
Node names of G and H can be changed by specifying the tuple
rename=('G-','H-') (for example). Node "u" in G is then renamed
"G-u" and "v" in H is renamed "H-v".
name : string
Specify the name for the union graph
Returns
-------
U : A union graph with the same type as G.
Notes
-----
To force a disjoint union with node relabeling, use
disjoint_union(G,H) or convert_node_labels_to integers().
Graph, edge, and node attributes are propagated from G and H
to the union graph. If a graph attribute is present in both
G and H the value from H is used.
See Also
--------
disjoint_union
"""
if not G.is_multigraph() == H.is_multigraph():
raise nx.NetworkXError("G and H must both be graphs or multigraphs.")
# Union is the same type as G
R = G.__class__()
# add graph attributes, H attributes take precedent over G attributes
R.graph.update(G.graph)
R.graph.update(H.graph)
# rename graph to obtain disjoint node labels
def add_prefix(graph, prefix):
if prefix is None:
return graph
def label(x):
if isinstance(x, str):
name = prefix + x
else:
name = prefix + repr(x)
return name
return nx.relabel_nodes(graph, label)
G = add_prefix(G, rename[0])
H = add_prefix(H, rename[1])
if set(G) & set(H):
raise nx.NetworkXError(
"The node sets of G and H are not disjoint.",
"Use appropriate rename=(Gprefix,Hprefix)" "or use disjoint_union(G,H).",
)
if G.is_multigraph():
G_edges = G.edges(keys=True, data=True)
else:
G_edges = G.edges(data=True)
if H.is_multigraph():
H_edges = H.edges(keys=True, data=True)
else:
H_edges = H.edges(data=True)
# add nodes
R.add_nodes_from(G)
R.add_nodes_from(H)
# add edges
R.add_edges_from(G_edges)
R.add_edges_from(H_edges)
# add node attributes
for n in G:
R.nodes[n].update(G.nodes[n])
for n in H:
R.nodes[n].update(H.nodes[n])
return R
[docs]def disjoint_union(G, H):
""" Return the disjoint union of graphs G and H.
This algorithm forces distinct integer node labels.
Parameters
----------
G,H : graph
A NetworkX graph
Returns
-------
U : A union graph with the same type as G.
Notes
-----
A new graph is created, of the same class as G. It is recommended
that G and H be either both directed or both undirected.
The nodes of G are relabeled 0 to len(G)-1, and the nodes of H are
relabeled len(G) to len(G)+len(H)-1.
Graph, edge, and node attributes are propagated from G and H
to the union graph. If a graph attribute is present in both
G and H the value from H is used.
"""
R1 = nx.convert_node_labels_to_integers(G)
R2 = nx.convert_node_labels_to_integers(H, first_label=len(R1))
R = union(R1, R2)
R.graph.update(G.graph)
R.graph.update(H.graph)
return R
[docs]def intersection(G, H):
"""Returns a new graph that contains only the edges that exist in
both G and H.
The node sets of H and G must be the same.
Parameters
----------
G,H : graph
A NetworkX graph. G and H must have the same node sets.
Returns
-------
GH : A new graph with the same type as G.
Notes
-----
Attributes from the graph, nodes, and edges are not copied to the new
graph. If you want a new graph of the intersection of G and H
with the attributes (including edge data) from G use remove_nodes_from()
as follows
>>> G = nx.path_graph(3)
>>> H = nx.path_graph(5)
>>> R = G.copy()
>>> R.remove_nodes_from(n for n in G if n not in H)
"""
# create new graph
R = nx.create_empty_copy(G)
if not G.is_multigraph() == H.is_multigraph():
raise nx.NetworkXError("G and H must both be graphs or multigraphs.")
if set(G) != set(H):
raise nx.NetworkXError("Node sets of graphs are not equal")
if G.number_of_edges() <= H.number_of_edges():
if G.is_multigraph():
edges = G.edges(keys=True)
else:
edges = G.edges()
for e in edges:
if H.has_edge(*e):
R.add_edge(*e)
else:
if H.is_multigraph():
edges = H.edges(keys=True)
else:
edges = H.edges()
for e in edges:
if G.has_edge(*e):
R.add_edge(*e)
return R
[docs]def difference(G, H):
"""Returns a new graph that contains the edges that exist in G but not in H.
The node sets of H and G must be the same.
Parameters
----------
G,H : graph
A NetworkX graph. G and H must have the same node sets.
Returns
-------
D : A new graph with the same type as G.
Notes
-----
Attributes from the graph, nodes, and edges are not copied to the new
graph. If you want a new graph of the difference of G and H with
with the attributes (including edge data) from G use remove_nodes_from()
as follows:
>>> G = nx.path_graph(3)
>>> H = nx.path_graph(5)
>>> R = G.copy()
>>> R.remove_nodes_from(n for n in G if n in H)
"""
# create new graph
if not G.is_multigraph() == H.is_multigraph():
raise nx.NetworkXError("G and H must both be graphs or multigraphs.")
R = nx.create_empty_copy(G)
if set(G) != set(H):
raise nx.NetworkXError("Node sets of graphs not equal")
if G.is_multigraph():
edges = G.edges(keys=True)
else:
edges = G.edges()
for e in edges:
if not H.has_edge(*e):
R.add_edge(*e)
return R
[docs]def symmetric_difference(G, H):
"""Returns new graph with edges that exist in either G or H but not both.
The node sets of H and G must be the same.
Parameters
----------
G,H : graph
A NetworkX graph. G and H must have the same node sets.
Returns
-------
D : A new graph with the same type as G.
Notes
-----
Attributes from the graph, nodes, and edges are not copied to the new
graph.
"""
# create new graph
if not G.is_multigraph() == H.is_multigraph():
raise nx.NetworkXError("G and H must both be graphs or multigraphs.")
R = nx.create_empty_copy(G)
if set(G) != set(H):
raise nx.NetworkXError("Node sets of graphs not equal")
gnodes = set(G) # set of nodes in G
hnodes = set(H) # set of nodes in H
nodes = gnodes.symmetric_difference(hnodes)
R.add_nodes_from(nodes)
if G.is_multigraph():
edges = G.edges(keys=True)
else:
edges = G.edges()
# we could copy the data here but then this function doesn't
# match intersection and difference
for e in edges:
if not H.has_edge(*e):
R.add_edge(*e)
if H.is_multigraph():
edges = H.edges(keys=True)
else:
edges = H.edges()
for e in edges:
if not G.has_edge(*e):
R.add_edge(*e)
return R
[docs]def compose(G, H):
"""Returns a new graph of G composed with H.
Composition is the simple union of the node sets and edge sets.
The node sets of G and H do not need to be disjoint.
Parameters
----------
G, H : graph
A NetworkX graph
Returns
-------
C: A new graph with the same type as G
Notes
-----
It is recommended that G and H be either both directed or both undirected.
Attributes from H take precedent over attributes from G.
For MultiGraphs, the edges are identified by incident nodes AND edge-key.
This can cause surprises (i.e., edge `(1, 2)` may or may not be the same
in two graphs) if you use MultiGraph without keeping track of edge keys.
"""
if not G.is_multigraph() == H.is_multigraph():
raise nx.NetworkXError("G and H must both be graphs or multigraphs.")
R = G.__class__()
# add graph attributes, H attributes take precedent over G attributes
R.graph.update(G.graph)
R.graph.update(H.graph)
R.add_nodes_from(G.nodes(data=True))
R.add_nodes_from(H.nodes(data=True))
if G.is_multigraph():
R.add_edges_from(G.edges(keys=True, data=True))
else:
R.add_edges_from(G.edges(data=True))
if H.is_multigraph():
R.add_edges_from(H.edges(keys=True, data=True))
else:
R.add_edges_from(H.edges(data=True))
return R
[docs]def full_join(G, H, rename=(None, None)):
"""Returns the full join of graphs G and H.
Full join is the union of G and H in which all edges between
G and H are added.
The node sets of G and H must be disjoint,
otherwise an exception is raised.
Parameters
----------
G, H : graph
A NetworkX graph
rename : bool , default=(None, None)
Node names of G and H can be changed by specifying the tuple
rename=('G-','H-') (for example). Node "u" in G is then renamed
"G-u" and "v" in H is renamed "H-v".
Returns
-------
U : The full join graph with the same type as G.
Notes
-----
It is recommended that G and H be either both directed or both undirected.
If G is directed, then edges from G to H are added as well as from H to G.
Note that full_join() does not produce parallel edges for MultiGraphs.
The full join operation of graphs G and H is the same as getting
their complement, performing a disjoint union, and finally getting
the complement of the resulting graph.
Graph, edge, and node attributes are propagated from G and H
to the union graph. If a graph attribute is present in both
G and H the value from H is used.
See Also
--------
union
disjoint_union
"""
R = union(G, H, rename)
def add_prefix(graph, prefix):
if prefix is None:
return graph
def label(x):
if isinstance(x, str):
name = prefix + x
else:
name = prefix + repr(x)
return name
return nx.relabel_nodes(graph, label)
G = add_prefix(G, rename[0])
H = add_prefix(H, rename[1])
for i in G:
for j in H:
R.add_edge(i, j)
if R.is_directed():
for i in H:
for j in G:
R.add_edge(i, j)
return R