airllm-env/lib/python3.11/site-packages/networkx/algorithms/boundary.py

"""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"]


@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)
    )


@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