# Source code for networkx.algorithms.boundary

```
"""Routines to find the boundary of a set of nodes.
An edge boundary is a set of edges, each of which has exactly one
endpoint in a given set of nodes (or, in the case of directed graphs,
the set of edges whose source node is in the set).
A node boundary of a set *S* of nodes is the set of (out-)neighbors of
nodes in *S* that are outside *S*.
"""
from itertools import chain
import networkx as nx
__all__ = ["edge_boundary", "node_boundary"]
[docs]
@nx._dispatchable(edge_attrs={"data": "default"}, preserve_edge_attrs="data")
def edge_boundary(G, nbunch1, nbunch2=None, data=False, keys=False, default=None):
"""Returns the edge boundary of `nbunch1`.
The *edge boundary* of a set *S* with respect to a set *T* is the
set of edges (*u*, *v*) such that *u* is in *S* and *v* is in *T*.
If *T* is not specified, it is assumed to be the set of all nodes
not in *S*.
Parameters
----------
G : NetworkX graph
nbunch1 : iterable
Iterable of nodes in the graph representing the set of nodes
whose edge boundary will be returned. (This is the set *S* from
the definition above.)
nbunch2 : iterable
Iterable of nodes representing the target (or "exterior") set of
nodes. (This is the set *T* from the definition above.) If not
specified, this is assumed to be the set of all nodes in `G`
not in `nbunch1`.
keys : bool
This parameter has the same meaning as in
:meth:`MultiGraph.edges`.
data : bool or object
This parameter has the same meaning as in
:meth:`MultiGraph.edges`.
default : object
This parameter has the same meaning as in
:meth:`MultiGraph.edges`.
Returns
-------
iterator
An iterator over the edges in the boundary of `nbunch1` with
respect to `nbunch2`. If `keys`, `data`, or `default`
are specified and `G` is a multigraph, then edges are returned
with keys and/or data, as in :meth:`MultiGraph.edges`.
Examples
--------
>>> G = nx.wheel_graph(6)
When nbunch2=None:
>>> list(nx.edge_boundary(G, (1, 3)))
[(1, 0), (1, 2), (1, 5), (3, 0), (3, 2), (3, 4)]
When nbunch2 is given:
>>> list(nx.edge_boundary(G, (1, 3), (2, 0)))
[(1, 0), (1, 2), (3, 0), (3, 2)]
Notes
-----
Any element of `nbunch` that is not in the graph `G` will be
ignored.
`nbunch1` and `nbunch2` are usually meant to be disjoint, but in
the interest of speed and generality, that is not required here.
"""
nset1 = {n for n in nbunch1 if n in G}
# Here we create an iterator over edges incident to nodes in the set
# `nset1`. The `Graph.edges()` method does not provide a guarantee
# on the orientation of the edges, so our algorithm below must
# handle the case in which exactly one orientation, either (u, v) or
# (v, u), appears in this iterable.
if G.is_multigraph():
edges = G.edges(nset1, data=data, keys=keys, default=default)
else:
edges = G.edges(nset1, data=data, default=default)
# If `nbunch2` is not provided, then it is assumed to be the set
# complement of `nbunch1`. For the sake of efficiency, this is
# implemented by using the `not in` operator, instead of by creating
# an additional set and using the `in` operator.
if nbunch2 is None:
return (e for e in edges if (e[0] in nset1) ^ (e[1] in nset1))
nset2 = set(nbunch2)
return (
e
for e in edges
if (e[0] in nset1 and e[1] in nset2) or (e[1] in nset1 and e[0] in nset2)
)
[docs]
@nx._dispatchable
def node_boundary(G, nbunch1, nbunch2=None):
"""Returns the node boundary of `nbunch1`.
The *node boundary* of a set *S* with respect to a set *T* is the
set of nodes *v* in *T* such that for some *u* in *S*, there is an
edge joining *u* to *v*. If *T* is not specified, it is assumed to
be the set of all nodes not in *S*.
Parameters
----------
G : NetworkX graph
nbunch1 : iterable
Iterable of nodes in the graph representing the set of nodes
whose node boundary will be returned. (This is the set *S* from
the definition above.)
nbunch2 : iterable
Iterable of nodes representing the target (or "exterior") set of
nodes. (This is the set *T* from the definition above.) If not
specified, this is assumed to be the set of all nodes in `G`
not in `nbunch1`.
Returns
-------
set
The node boundary of `nbunch1` with respect to `nbunch2`.
Examples
--------
>>> G = nx.wheel_graph(6)
When nbunch2=None:
>>> list(nx.node_boundary(G, (3, 4)))
[0, 2, 5]
When nbunch2 is given:
>>> list(nx.node_boundary(G, (3, 4), (0, 1, 5)))
[0, 5]
Notes
-----
Any element of `nbunch` that is not in the graph `G` will be
ignored.
`nbunch1` and `nbunch2` are usually meant to be disjoint, but in
the interest of speed and generality, that is not required here.
"""
nset1 = {n for n in nbunch1 if n in G}
bdy = set(chain.from_iterable(G[v] for v in nset1)) - nset1
# If `nbunch2` is not specified, it is assumed to be the set
# complement of `nbunch1`.
if nbunch2 is not None:
bdy &= set(nbunch2)
return bdy
```