283 lines
9.7 KiB
Python
283 lines
9.7 KiB
Python
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import networkx as nx
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__all__ = ["convert_node_labels_to_integers", "relabel_nodes"]
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def relabel_nodes(G, mapping, copy=True):
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"""Relabel the nodes of the graph G.
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Parameters
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----------
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G : graph
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A NetworkX graph
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mapping : dictionary
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A dictionary with the old labels as keys and new labels as values.
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A partial mapping is allowed. Mapping 2 nodes to a single node is allowed.
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copy : bool (optional, default=True)
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If True return a copy, or if False relabel the nodes in place.
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Examples
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--------
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To create a new graph with nodes relabeled according to a given
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dictionary:
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>>> G = nx.path_graph(3)
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>>> sorted(G)
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[0, 1, 2]
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>>> mapping = {0: "a", 1: "b", 2: "c"}
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>>> H = nx.relabel_nodes(G, mapping)
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>>> sorted(H)
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['a', 'b', 'c']
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Nodes can be relabeled with any hashable object, including numbers
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and strings:
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>>> import string
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>>> G = nx.path_graph(26) # nodes are integers 0 through 25
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>>> sorted(G)[:3]
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[0, 1, 2]
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>>> mapping = dict(zip(G, string.ascii_lowercase))
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>>> G = nx.relabel_nodes(G, mapping) # nodes are characters a through z
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>>> sorted(G)[:3]
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['a', 'b', 'c']
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>>> mapping = dict(zip(G, range(1, 27)))
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>>> G = nx.relabel_nodes(G, mapping) # nodes are integers 1 through 26
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>>> sorted(G)[:3]
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[1, 2, 3]
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To perform a partial in-place relabeling, provide a dictionary
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mapping only a subset of the nodes, and set the `copy` keyword
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argument to False:
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>>> G = nx.path_graph(3) # nodes 0-1-2
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>>> mapping = {0: "a", 1: "b"} # 0->'a' and 1->'b'
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>>> G = nx.relabel_nodes(G, mapping, copy=False)
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>>> sorted(G, key=str)
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[2, 'a', 'b']
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A mapping can also be given as a function:
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>>> G = nx.path_graph(3)
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>>> H = nx.relabel_nodes(G, lambda x: x ** 2)
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>>> list(H)
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[0, 1, 4]
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In a multigraph, relabeling two or more nodes to the same new node
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will retain all edges, but may change the edge keys in the process:
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>>> G = nx.MultiGraph()
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>>> G.add_edge(0, 1, value="a") # returns the key for this edge
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0
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>>> G.add_edge(0, 2, value="b")
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0
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>>> G.add_edge(0, 3, value="c")
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0
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>>> mapping = {1: 4, 2: 4, 3: 4}
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>>> H = nx.relabel_nodes(G, mapping, copy=True)
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>>> print(H[0])
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{4: {0: {'value': 'a'}, 1: {'value': 'b'}, 2: {'value': 'c'}}}
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This works for in-place relabeling too:
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>>> G = nx.relabel_nodes(G, mapping, copy=False)
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>>> print(G[0])
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{4: {0: {'value': 'a'}, 1: {'value': 'b'}, 2: {'value': 'c'}}}
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Notes
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-----
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Only the nodes specified in the mapping will be relabeled.
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The keyword setting copy=False modifies the graph in place.
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Relabel_nodes avoids naming collisions by building a
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directed graph from ``mapping`` which specifies the order of
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relabelings. Naming collisions, such as a->b, b->c, are ordered
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such that "b" gets renamed to "c" before "a" gets renamed "b".
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In cases of circular mappings (e.g. a->b, b->a), modifying the
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graph is not possible in-place and an exception is raised.
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In that case, use copy=True.
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If a relabel operation on a multigraph would cause two or more
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edges to have the same source, target and key, the second edge must
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be assigned a new key to retain all edges. The new key is set
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to the lowest non-negative integer not already used as a key
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for edges between these two nodes. Note that this means non-numeric
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keys may be replaced by numeric keys.
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See Also
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--------
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convert_node_labels_to_integers
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"""
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# you can pass a function f(old_label)->new_label
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# but we'll just make a dictionary here regardless
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if not hasattr(mapping, "__getitem__"):
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m = {n: mapping(n) for n in G}
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else:
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m = mapping
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if copy:
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return _relabel_copy(G, m)
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else:
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return _relabel_inplace(G, m)
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def _relabel_inplace(G, mapping):
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old_labels = set(mapping.keys())
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new_labels = set(mapping.values())
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if len(old_labels & new_labels) > 0:
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# labels sets overlap
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# can we topological sort and still do the relabeling?
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D = nx.DiGraph(list(mapping.items()))
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D.remove_edges_from(nx.selfloop_edges(D))
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try:
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nodes = reversed(list(nx.topological_sort(D)))
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except nx.NetworkXUnfeasible as e:
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raise nx.NetworkXUnfeasible(
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"The node label sets are overlapping and no ordering can "
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"resolve the mapping. Use copy=True."
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) from e
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else:
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# non-overlapping label sets
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nodes = old_labels
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multigraph = G.is_multigraph()
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directed = G.is_directed()
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for old in nodes:
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try:
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new = mapping[old]
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except KeyError:
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continue
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if new == old:
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continue
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try:
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G.add_node(new, **G.nodes[old])
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except KeyError as e:
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raise KeyError(f"Node {old} is not in the graph") from e
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if multigraph:
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new_edges = [
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(new, new if old == target else target, key, data)
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for (_, target, key, data) in G.edges(old, data=True, keys=True)
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]
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if directed:
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new_edges += [
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(new if old == source else source, new, key, data)
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for (source, _, key, data) in G.in_edges(old, data=True, keys=True)
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]
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# Ensure new edges won't overwrite existing ones
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seen = set()
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for i, (source, target, key, data) in enumerate(new_edges):
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if target in G[source] and key in G[source][target]:
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new_key = 0 if not isinstance(key, (int, float)) else key
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while new_key in G[source][target] or (target, new_key) in seen:
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new_key += 1
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new_edges[i] = (source, target, new_key, data)
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seen.add((target, new_key))
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else:
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new_edges = [
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(new, new if old == target else target, data)
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for (_, target, data) in G.edges(old, data=True)
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]
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if directed:
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new_edges += [
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(new if old == source else source, new, data)
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for (source, _, data) in G.in_edges(old, data=True)
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]
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G.remove_node(old)
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G.add_edges_from(new_edges)
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return G
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def _relabel_copy(G, mapping):
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H = G.__class__()
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H.add_nodes_from(mapping.get(n, n) for n in G)
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H._node.update((mapping.get(n, n), d.copy()) for n, d in G.nodes.items())
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if G.is_multigraph():
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new_edges = [
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(mapping.get(n1, n1), mapping.get(n2, n2), k, d.copy())
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for (n1, n2, k, d) in G.edges(keys=True, data=True)
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]
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# check for conflicting edge-keys
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undirected = not G.is_directed()
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seen_edges = set()
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for i, (source, target, key, data) in enumerate(new_edges):
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while (source, target, key) in seen_edges:
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if not isinstance(key, (int, float)):
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key = 0
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key += 1
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seen_edges.add((source, target, key))
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if undirected:
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seen_edges.add((target, source, key))
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new_edges[i] = (source, target, key, data)
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H.add_edges_from(new_edges)
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else:
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H.add_edges_from(
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(mapping.get(n1, n1), mapping.get(n2, n2), d.copy())
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for (n1, n2, d) in G.edges(data=True)
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)
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H.graph.update(G.graph)
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return H
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def convert_node_labels_to_integers(
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G, first_label=0, ordering="default", label_attribute=None
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):
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"""Returns a copy of the graph G with the nodes relabeled using
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consecutive integers.
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Parameters
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----------
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G : graph
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A NetworkX graph
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first_label : int, optional (default=0)
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An integer specifying the starting offset in numbering nodes.
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The new integer labels are numbered first_label, ..., n-1+first_label.
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ordering : string
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"default" : inherit node ordering from G.nodes()
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"sorted" : inherit node ordering from sorted(G.nodes())
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"increasing degree" : nodes are sorted by increasing degree
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"decreasing degree" : nodes are sorted by decreasing degree
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label_attribute : string, optional (default=None)
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Name of node attribute to store old label. If None no attribute
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is created.
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Notes
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-----
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Node and edge attribute data are copied to the new (relabeled) graph.
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There is no guarantee that the relabeling of nodes to integers will
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give the same two integers for two (even identical graphs).
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Use the `ordering` argument to try to preserve the order.
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See Also
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--------
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relabel_nodes
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"""
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N = G.number_of_nodes() + first_label
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if ordering == "default":
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mapping = dict(zip(G.nodes(), range(first_label, N)))
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elif ordering == "sorted":
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nlist = sorted(G.nodes())
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mapping = dict(zip(nlist, range(first_label, N)))
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elif ordering == "increasing degree":
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dv_pairs = [(d, n) for (n, d) in G.degree()]
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dv_pairs.sort() # in-place sort from lowest to highest degree
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mapping = dict(zip([n for d, n in dv_pairs], range(first_label, N)))
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elif ordering == "decreasing degree":
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dv_pairs = [(d, n) for (n, d) in G.degree()]
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dv_pairs.sort() # in-place sort from lowest to highest degree
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dv_pairs.reverse()
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mapping = dict(zip([n for d, n in dv_pairs], range(first_label, N)))
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else:
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raise nx.NetworkXError(f"Unknown node ordering: {ordering}")
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H = relabel_nodes(G, mapping)
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# create node attribute with the old label
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if label_attribute is not None:
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nx.set_node_attributes(H, {v: k for k, v in mapping.items()}, label_attribute)
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return H
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