411 lines
11 KiB
Python
411 lines
11 KiB
Python
# Original author: D. Eppstein, UC Irvine, August 12, 2003.
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# The original code at http://www.ics.uci.edu/~eppstein/PADS/ is public domain.
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# Copyright (C) 2004-2019 by
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# Aric Hagberg <hagberg@lanl.gov>
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# Dan Schult <dschult@colgate.edu>
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# Pieter Swart <swart@lanl.gov>
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# Tomas Gavenciak <gavento@ucw.cz>
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# All rights reserved.
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# BSD license.
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#
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# Authors: Tomas Gavenciak <gavento@ucw.cz>
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# Aric Hagberg <aric.hagberg@lanl.gov>
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"""Functions for reading and writing graphs in the *graph6* format.
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The *graph6* file format is suitable for small graphs or large dense
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graphs. For large sparse graphs, use the *sparse6* format.
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For more information, see the `graph6`_ homepage.
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.. _graph6: http://users.cecs.anu.edu.au/~bdm/data/formats.html
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"""
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from itertools import islice
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import sys
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import networkx as nx
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from networkx.exception import NetworkXError
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from networkx.utils import open_file, not_implemented_for
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__all__ = ['from_graph6_bytes', 'read_graph6', 'to_graph6_bytes',
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'write_graph6']
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def _generate_graph6_bytes(G, nodes, header):
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"""Yield bytes in the graph6 encoding of a graph.
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`G` is an undirected simple graph. `nodes` is the list of nodes for
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which the node-induced subgraph will be encoded; if `nodes` is the
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list of all nodes in the graph, the entire graph will be
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encoded. `header` is a Boolean that specifies whether to generate
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the header ``b'>>graph6<<'`` before the remaining data.
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This function generates `bytes` objects in the following order:
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1. the header (if requested),
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2. the encoding of the number of nodes,
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3. each character, one-at-a-time, in the encoding of the requested
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node-induced subgraph,
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4. a newline character.
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This function raises :exc:`ValueError` if the graph is too large for
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the graph6 format (that is, greater than ``2 ** 36`` nodes).
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"""
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n = len(G)
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if n >= 2 ** 36:
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raise ValueError('graph6 is only defined if number of nodes is less '
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'than 2 ** 36')
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if header:
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yield b'>>graph6<<'
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for d in n_to_data(n):
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yield str.encode(chr(d + 63))
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# This generates the same as `(v in G[u] for u, v in combinations(G, 2))`,
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# but in "column-major" order instead of "row-major" order.
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bits = (nodes[j] in G[nodes[i]] for j in range(1, n) for i in range(j))
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chunk = list(islice(bits, 6))
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while chunk:
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d = sum(b << 5 - i for i, b in enumerate(chunk))
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yield str.encode(chr(d + 63))
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chunk = list(islice(bits, 6))
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yield b'\n'
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def from_graph6_bytes(string):
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"""Read a simple undirected graph in graph6 format from string.
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Parameters
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----------
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string : string
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Data in graph6 format, without a trailing newline.
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Returns
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-------
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G : Graph
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Raises
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------
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NetworkXError
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If the string is unable to be parsed in graph6 format
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ValueError
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If any character ``c`` in the input string does not satisfy
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``63 <= ord(c) < 127``.
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Examples
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--------
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>>> G = nx.from_graph6_bytes(b'A_')
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>>> sorted(G.edges())
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[(0, 1)]
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See Also
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--------
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read_graph6, write_graph6
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References
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----------
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.. [1] Graph6 specification
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<http://users.cecs.anu.edu.au/~bdm/data/formats.html>
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"""
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def bits():
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"""Returns sequence of individual bits from 6-bit-per-value
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list of data values."""
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for d in data:
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for i in [5, 4, 3, 2, 1, 0]:
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yield (d >> i) & 1
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if string.startswith(b'>>graph6<<'):
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string = string[10:]
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if sys.version_info < (3, ):
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data = [ord(c) - 63 for c in string]
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else:
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data = [c - 63 for c in string]
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if any(c > 63 for c in data):
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raise ValueError('each input character must be in range(63, 127)')
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n, data = data_to_n(data)
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nd = (n * (n - 1) // 2 + 5) // 6
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if len(data) != nd:
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raise NetworkXError(
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'Expected %d bits but got %d in graph6' % (n * (n - 1) // 2, len(data) * 6))
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G = nx.Graph()
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G.add_nodes_from(range(n))
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for (i, j), b in zip([(i, j) for j in range(1, n) for i in range(j)], bits()):
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if b:
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G.add_edge(i, j)
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return G
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def to_graph6_bytes(G, nodes=None, header=True):
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"""Convert a simple undirected graph to bytes in graph6 format.
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Parameters
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----------
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G : Graph (undirected)
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nodes: list or iterable
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Nodes are labeled 0...n-1 in the order provided. If None the ordering
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given by ``G.nodes()`` is used.
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header: bool
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If True add '>>graph6<<' bytes to head of data.
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Raises
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------
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NetworkXNotImplemented
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If the graph is directed or is a multigraph.
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ValueError
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If the graph has at least ``2 ** 36`` nodes; the graph6 format
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is only defined for graphs of order less than ``2 ** 36``.
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Examples
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--------
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>>> nx.to_graph6_bytes(nx.path_graph(2)) # doctest: +SKIP
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b'>>graph6<<A_\\n'
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See Also
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--------
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from_graph6_bytes, read_graph6, write_graph6_bytes
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Notes
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-----
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The returned bytes end with a newline character.
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The format does not support edge or node labels, parallel edges or
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self loops. If self loops are present they are silently ignored.
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References
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----------
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.. [1] Graph6 specification
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<http://users.cecs.anu.edu.au/~bdm/data/formats.html>
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"""
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if nodes is not None:
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G = G.subgraph(nodes)
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H = nx.convert_node_labels_to_integers(G)
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nodes = sorted(H.nodes())
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return b''.join(_generate_graph6_bytes(H, nodes, header))
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@open_file(0, mode='rb')
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def read_graph6(path):
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"""Read simple undirected graphs in graph6 format from path.
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Parameters
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----------
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path : file or string
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File or filename to write.
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Returns
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-------
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G : Graph or list of Graphs
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If the file contains multiple lines then a list of graphs is returned
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Raises
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------
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NetworkXError
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If the string is unable to be parsed in graph6 format
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Examples
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--------
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You can read a graph6 file by giving the path to the file::
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>>> import tempfile
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>>> with tempfile.NamedTemporaryFile() as f:
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... _ = f.write(b'>>graph6<<A_\\n')
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... _ = f.seek(0)
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... G = nx.read_graph6(f.name)
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>>> list(G.edges())
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[(0, 1)]
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You can also read a graph6 file by giving an open file-like object::
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>>> import tempfile
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>>> with tempfile.NamedTemporaryFile() as f:
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... _ = f.write(b'>>graph6<<A_\\n')
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... _ = f.seek(0)
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... G = nx.read_graph6(f)
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>>> list(G.edges())
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[(0, 1)]
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See Also
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--------
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from_graph6_bytes, write_graph6
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References
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----------
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.. [1] Graph6 specification
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<http://users.cecs.anu.edu.au/~bdm/data/formats.html>
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"""
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glist = []
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for line in path:
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line = line.strip()
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if not len(line):
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continue
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glist.append(from_graph6_bytes(line))
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if len(glist) == 1:
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return glist[0]
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else:
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return glist
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@not_implemented_for('directed')
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@not_implemented_for('multigraph')
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@open_file(1, mode='wb')
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def write_graph6(G, path, nodes=None, header=True):
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"""Write a simple undirected graph to a path in graph6 format.
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Parameters
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----------
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G : Graph (undirected)
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path : str
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The path naming the file to which to write the graph.
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nodes: list or iterable
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Nodes are labeled 0...n-1 in the order provided. If None the ordering
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given by ``G.nodes()`` is used.
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header: bool
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If True add '>>graph6<<' string to head of data
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Raises
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------
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NetworkXNotImplemented
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If the graph is directed or is a multigraph.
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ValueError
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If the graph has at least ``2 ** 36`` nodes; the graph6 format
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is only defined for graphs of order less than ``2 ** 36``.
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Examples
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--------
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You can write a graph6 file by giving the path to a file::
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>>> import tempfile
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>>> with tempfile.NamedTemporaryFile() as f:
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... nx.write_graph6(nx.path_graph(2), f.name)
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... _ = f.seek(0)
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... print(f.read()) # doctest: +SKIP
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b'>>graph6<<A_\\n'
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See Also
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--------
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from_graph6_bytes, read_graph6
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Notes
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-----
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The function writes a newline character after writing the encoding
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of the graph.
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The format does not support edge or node labels, parallel edges or
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self loops. If self loops are present they are silently ignored.
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References
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----------
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.. [1] Graph6 specification
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<http://users.cecs.anu.edu.au/~bdm/data/formats.html>
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"""
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return write_graph6_file(G, path, nodes=nodes, header=header)
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@not_implemented_for('directed')
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@not_implemented_for('multigraph')
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def write_graph6_file(G, f, nodes=None, header=True):
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"""Write a simple undirected graph to a file-like object in graph6 format.
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Parameters
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----------
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G : Graph (undirected)
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f : file-like object
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The file to write.
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nodes: list or iterable
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Nodes are labeled 0...n-1 in the order provided. If None the ordering
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given by ``G.nodes()`` is used.
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header: bool
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If True add '>>graph6<<' string to head of data
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Raises
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------
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NetworkXNotImplemented
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If the graph is directed or is a multigraph.
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ValueError
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If the graph has at least ``2 ** 36`` nodes; the graph6 format
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is only defined for graphs of order less than ``2 ** 36``.
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Examples
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--------
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You can write a graph6 file by giving an open file-like object::
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>>> import tempfile
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>>> with tempfile.NamedTemporaryFile() as f:
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... nx.write_graph6(nx.path_graph(2), f)
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... _ = f.seek(0)
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... print(f.read()) # doctest: +SKIP
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b'>>graph6<<A_\\n'
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See Also
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--------
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from_graph6_bytes, read_graph6
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Notes
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-----
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The function writes a newline character after writing the encoding
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of the graph.
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The format does not support edge or node labels, parallel edges or
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self loops. If self loops are present they are silently ignored.
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References
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----------
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.. [1] Graph6 specification
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<http://users.cecs.anu.edu.au/~bdm/data/formats.html>
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"""
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if nodes is not None:
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G = G.subgraph(nodes)
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H = nx.convert_node_labels_to_integers(G)
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nodes = sorted(H.nodes())
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for b in _generate_graph6_bytes(H, nodes, header):
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f.write(b)
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def data_to_n(data):
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"""Read initial one-, four- or eight-unit value from graph6
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integer sequence.
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Return (value, rest of seq.)"""
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if data[0] <= 62:
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return data[0], data[1:]
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if data[1] <= 62:
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return (data[1] << 12) + (data[2] << 6) + data[3], data[4:]
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return ((data[2] << 30) + (data[3] << 24) + (data[4] << 18) +
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(data[5] << 12) + (data[6] << 6) + data[7], data[8:])
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def n_to_data(n):
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"""Convert an integer to one-, four- or eight-unit graph6 sequence.
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This function is undefined if `n` is not in ``range(2 ** 36)``.
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"""
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if n <= 62:
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return [n]
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elif n <= 258047:
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return [63, (n >> 12) & 0x3f, (n >> 6) & 0x3f, n & 0x3f]
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else: # if n <= 68719476735:
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return [63, 63,
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(n >> 30) & 0x3f, (n >> 24) & 0x3f, (n >> 18) & 0x3f,
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(n >> 12) & 0x3f, (n >> 6) & 0x3f, n & 0x3f]
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