# Source code for networkx.algorithms.operators.all

```"""Operations on many graphs.
"""
from itertools import chain, repeat

import networkx as nx

__all__ = ["union_all", "compose_all", "disjoint_union_all", "intersection_all"]

[docs]
@nx._dispatchable(graphs="[graphs]", preserve_all_attrs=True, returns_graph=True)
def union_all(graphs, rename=()):
"""Returns the union of all graphs.

The graphs must be disjoint, otherwise an exception is raised.

Parameters
----------
graphs : iterable
Iterable of NetworkX graphs

rename : iterable , optional
Node names of graphs 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". Infinite generators (like itertools.count)
are also supported.

Returns
-------
U : a graph with the same type as the first graph in list

Raises
------
ValueError
If `graphs` is an empty list.

NetworkXError
In case of mixed type graphs, like MultiGraph and Graph, or directed and undirected graphs.

Notes
-----
For operating on mixed type graphs, they should be converted to the same type.
>>> G = nx.Graph()
>>> H = nx.DiGraph()
>>> GH = union_all([nx.DiGraph(G), H])

To force a disjoint union with node relabeling, use
disjoint_union_all(G,H) or convert_node_labels_to integers().

Graph, edge, and node attributes are propagated to the union graph.
If a graph attribute is present in multiple graphs, then the value
from the last graph in the list with that attribute is used.

Examples
--------
>>> G1 = nx.Graph([(1, 2), (2, 3)])
>>> G2 = nx.Graph([(4, 5), (5, 6)])
>>> result_graph = nx.union_all([G1, G2])
>>> result_graph.nodes()
NodeView((1, 2, 3, 4, 5, 6))
>>> result_graph.edges()
EdgeView([(1, 2), (2, 3), (4, 5), (5, 6)])

--------
union
disjoint_union_all
"""
R = None
seen_nodes = set()

# rename graph to obtain disjoint node labels
if prefix is None:
return graph

def label(x):
return f"{prefix}{x}"

return nx.relabel_nodes(graph, label)

rename = chain(rename, repeat(None))
graphs = (add_prefix(G, name) for G, name in zip(graphs, rename))

for i, G in enumerate(graphs):
G_nodes_set = set(G.nodes)
if i == 0:
# Union is the same type as first graph
R = G.__class__()
elif G.is_directed() != R.is_directed():
raise nx.NetworkXError("All graphs must be directed or undirected.")
elif G.is_multigraph() != R.is_multigraph():
raise nx.NetworkXError("All graphs must be graphs or multigraphs.")
elif not seen_nodes.isdisjoint(G_nodes_set):
raise nx.NetworkXError(
"The node sets of the graphs are not disjoint.\n"
"Use `rename` to specify prefixes for the graphs or use\n"
"disjoint_union(G1, G2, ..., GN)."
)

seen_nodes |= G_nodes_set
R.graph.update(G.graph)
G.edges(keys=True, data=True) if G.is_multigraph() else G.edges(data=True)
)

if R is None:
raise ValueError("cannot apply union_all to an empty list")

return R

[docs]
@nx._dispatchable(graphs="[graphs]", preserve_all_attrs=True, returns_graph=True)
def disjoint_union_all(graphs):
"""Returns the disjoint union of all graphs.

This operation forces distinct integer node labels starting with 0
for the first graph in the list and numbering consecutively.

Parameters
----------
graphs : iterable
Iterable of NetworkX graphs

Returns
-------
U : A graph with the same type as the first graph in list

Raises
------
ValueError
If `graphs` is an empty list.

NetworkXError
In case of mixed type graphs, like MultiGraph and Graph, or directed and undirected graphs.

Examples
--------
>>> G1 = nx.Graph([(1, 2), (2, 3)])
>>> G2 = nx.Graph([(4, 5), (5, 6)])
>>> U = nx.disjoint_union_all([G1, G2])
>>> list(U.nodes())
[0, 1, 2, 3, 4, 5]
>>> list(U.edges())
[(0, 1), (1, 2), (3, 4), (4, 5)]

Notes
-----
For operating on mixed type graphs, they should be converted to the same type.

Graph, edge, and node attributes are propagated to the union graph.
If a graph attribute is present in multiple graphs, then the value
from the last graph in the list with that attribute is used.
"""

def yield_relabeled(graphs):
first_label = 0
for G in graphs:
yield nx.convert_node_labels_to_integers(G, first_label=first_label)
first_label += len(G)

R = union_all(yield_relabeled(graphs))

return R

[docs]
@nx._dispatchable(graphs="[graphs]", preserve_all_attrs=True, returns_graph=True)
def compose_all(graphs):
"""Returns the composition of all graphs.

Composition is the simple union of the node sets and edge sets.
The node sets of the supplied graphs need not be disjoint.

Parameters
----------
graphs : iterable
Iterable of NetworkX graphs

Returns
-------
C : A graph with the same type as the first graph in list

Raises
------
ValueError
If `graphs` is an empty list.

NetworkXError
In case of mixed type graphs, like MultiGraph and Graph, or directed and undirected graphs.

Examples
--------
>>> G1 = nx.Graph([(1, 2), (2, 3)])
>>> G2 = nx.Graph([(3, 4), (5, 6)])
>>> C = nx.compose_all([G1, G2])
>>> list(C.nodes())
[1, 2, 3, 4, 5, 6]
>>> list(C.edges())
[(1, 2), (2, 3), (3, 4), (5, 6)]

Notes
-----
For operating on mixed type graphs, they should be converted to the same type.

Graph, edge, and node attributes are propagated to the union graph.
If a graph attribute is present in multiple graphs, then the value
from the last graph in the list with that attribute is used.
"""
R = None

# add graph attributes, H attributes take precedent over G attributes
for i, G in enumerate(graphs):
if i == 0:
# create new graph
R = G.__class__()
elif G.is_directed() != R.is_directed():
raise nx.NetworkXError("All graphs must be directed or undirected.")
elif G.is_multigraph() != R.is_multigraph():
raise nx.NetworkXError("All graphs must be graphs or multigraphs.")

R.graph.update(G.graph)
G.edges(keys=True, data=True) if G.is_multigraph() else G.edges(data=True)
)

if R is None:
raise ValueError("cannot apply compose_all to an empty list")

return R

[docs]
@nx._dispatchable(graphs="[graphs]", returns_graph=True)
def intersection_all(graphs):
"""Returns a new graph that contains only the nodes and the edges that exist in
all graphs.

Parameters
----------
graphs : iterable
Iterable of NetworkX graphs

Returns
-------
R : A new graph with the same type as the first graph in list

Raises
------
ValueError
If `graphs` is an empty list.

NetworkXError
In case of mixed type graphs, like MultiGraph and Graph, or directed and undirected graphs.

Notes
-----
For operating on mixed type graphs, they should be converted to the same type.

Attributes from the graph, nodes, and edges are not copied to the new
graph.

The resulting graph can be updated with attributes if desired. For example, code which adds the minimum attribute for each node across all graphs could work.
>>> g = nx.Graph()

>>> h = g.copy()
>>> h.nodes[0]["capacity"] = 2

>>> gh = nx.intersection_all([g, h])

>>> new_node_attr = {
...     n: min(*(anyG.nodes[n].get("capacity", float("inf")) for anyG in [g, h]))
...     for n in gh
... }
>>> nx.set_node_attributes(gh, new_node_attr, "new_capacity")
>>> gh.nodes(data=True)
NodeDataView({0: {'new_capacity': 2}, 1: {'new_capacity': 3}})

Examples
--------
>>> G1 = nx.Graph([(1, 2), (2, 3)])
>>> G2 = nx.Graph([(2, 3), (3, 4)])
>>> R = nx.intersection_all([G1, G2])
>>> list(R.nodes())
[2, 3]
>>> list(R.edges())
[(2, 3)]

"""
R = None

for i, G in enumerate(graphs):
G_nodes_set = set(G.nodes)
G_edges_set = set(G.edges)
if not G.is_directed():
if G.is_multigraph():
G_edges_set.update((v, u, k) for u, v, k in list(G_edges_set))
else:
G_edges_set.update((v, u) for u, v in list(G_edges_set))
if i == 0:
# create new graph
R = G.__class__()
node_intersection = G_nodes_set
edge_intersection = G_edges_set
elif G.is_directed() != R.is_directed():
raise nx.NetworkXError("All graphs must be directed or undirected.")
elif G.is_multigraph() != R.is_multigraph():
raise nx.NetworkXError("All graphs must be graphs or multigraphs.")
else:
node_intersection &= G_nodes_set
edge_intersection &= G_edges_set

if R is None:
raise ValueError("cannot apply intersection_all to an empty list")