# Original author: D. Eppstein, UC Irvine, August 12, 2003. # The original code at http://www.ics.uci.edu/~eppstein/PADS/ is public domain. """Functions for reading and writing graphs in the *graph6* format. The *graph6* file format is suitable for small graphs or large dense graphs. For large sparse graphs, use the *sparse6* format. For more information, see the `graph6`_ homepage. .. _graph6: http://users.cecs.anu.edu.au/~bdm/data/formats.html """ from itertools import islice import networkx as nx from networkx.exception import NetworkXError from networkx.utils import open_file, not_implemented_for __all__ = ["from_graph6_bytes", "read_graph6", "to_graph6_bytes", "write_graph6"] def _generate_graph6_bytes(G, nodes, header): """Yield bytes in the graph6 encoding of a graph. `G` is an undirected simple graph. `nodes` is the list of nodes for which the node-induced subgraph will be encoded; if `nodes` is the list of all nodes in the graph, the entire graph will be encoded. `header` is a Boolean that specifies whether to generate the header ``b'>>graph6<<'`` before the remaining data. This function generates `bytes` objects in the following order: 1. the header (if requested), 2. the encoding of the number of nodes, 3. each character, one-at-a-time, in the encoding of the requested node-induced subgraph, 4. a newline character. This function raises :exc:`ValueError` if the graph is too large for the graph6 format (that is, greater than ``2 ** 36`` nodes). """ n = len(G) if n >= 2 ** 36: raise ValueError( "graph6 is only defined if number of nodes is less " "than 2 ** 36" ) if header: yield b">>graph6<<" for d in n_to_data(n): yield str.encode(chr(d + 63)) # This generates the same as `(v in G[u] for u, v in combinations(G, 2))`, # but in "column-major" order instead of "row-major" order. bits = (nodes[j] in G[nodes[i]] for j in range(1, n) for i in range(j)) chunk = list(islice(bits, 6)) while chunk: d = sum(b << 5 - i for i, b in enumerate(chunk)) yield str.encode(chr(d + 63)) chunk = list(islice(bits, 6)) yield b"\n" def from_graph6_bytes(bytes_in): """Read a simple undirected graph in graph6 format from bytes. Parameters ---------- bytes_in : bytes Data in graph6 format, without a trailing newline. Returns ------- G : Graph Raises ------ NetworkXError If bytes_in is unable to be parsed in graph6 format ValueError If any character ``c`` in bytes_in does not satisfy ``63 <= ord(c) < 127``. Examples -------- >>> G = nx.from_graph6_bytes(b"A_") >>> sorted(G.edges()) [(0, 1)] See Also -------- read_graph6, write_graph6 References ---------- .. [1] Graph6 specification """ def bits(): """Returns sequence of individual bits from 6-bit-per-value list of data values.""" for d in data: for i in [5, 4, 3, 2, 1, 0]: yield (d >> i) & 1 if bytes_in.startswith(b">>graph6<<"): bytes_in = bytes_in[10:] data = [c - 63 for c in bytes_in] if any(c > 63 for c in data): raise ValueError("each input character must be in range(63, 127)") n, data = data_to_n(data) nd = (n * (n - 1) // 2 + 5) // 6 if len(data) != nd: raise NetworkXError( f"Expected {n * (n - 1) // 2} bits but got {len(data) * 6} in graph6" ) G = nx.Graph() G.add_nodes_from(range(n)) for (i, j), b in zip([(i, j) for j in range(1, n) for i in range(j)], bits()): if b: G.add_edge(i, j) return G def to_graph6_bytes(G, nodes=None, header=True): """Convert a simple undirected graph to bytes in graph6 format. Parameters ---------- G : Graph (undirected) nodes: list or iterable Nodes are labeled 0...n-1 in the order provided. If None the ordering given by ``G.nodes()`` is used. header: bool If True add '>>graph6<<' bytes to head of data. Raises ------ NetworkXNotImplemented If the graph is directed or is a multigraph. ValueError If the graph has at least ``2 ** 36`` nodes; the graph6 format is only defined for graphs of order less than ``2 ** 36``. Examples -------- >>> nx.to_graph6_bytes(nx.path_graph(2)) b'>>graph6< """ if nodes is not None: G = G.subgraph(nodes) H = nx.convert_node_labels_to_integers(G) nodes = sorted(H.nodes()) return b"".join(_generate_graph6_bytes(H, nodes, header)) @open_file(0, mode="rb") def read_graph6(path): """Read simple undirected graphs in graph6 format from path. Parameters ---------- path : file or string File or filename to write. Returns ------- G : Graph or list of Graphs If the file contains multiple lines then a list of graphs is returned Raises ------ NetworkXError If the string is unable to be parsed in graph6 format Examples -------- You can read a graph6 file by giving the path to the file:: >>> import tempfile >>> with tempfile.NamedTemporaryFile() as f: ... _ = f.write(b">>graph6<>> list(G.edges()) [(0, 1)] You can also read a graph6 file by giving an open file-like object:: >>> import tempfile >>> with tempfile.NamedTemporaryFile() as f: ... _ = f.write(b">>graph6<>> list(G.edges()) [(0, 1)] See Also -------- from_graph6_bytes, write_graph6 References ---------- .. [1] Graph6 specification """ glist = [] for line in path: line = line.strip() if not len(line): continue glist.append(from_graph6_bytes(line)) if len(glist) == 1: return glist[0] else: return glist @not_implemented_for("directed") @not_implemented_for("multigraph") @open_file(1, mode="wb") def write_graph6(G, path, nodes=None, header=True): """Write a simple undirected graph to a path in graph6 format. Parameters ---------- G : Graph (undirected) path : str The path naming the file to which to write the graph. nodes: list or iterable Nodes are labeled 0...n-1 in the order provided. If None the ordering given by ``G.nodes()`` is used. header: bool If True add '>>graph6<<' string to head of data Raises ------ NetworkXNotImplemented If the graph is directed or is a multigraph. ValueError If the graph has at least ``2 ** 36`` nodes; the graph6 format is only defined for graphs of order less than ``2 ** 36``. Examples -------- You can write a graph6 file by giving the path to a file:: >>> import tempfile >>> with tempfile.NamedTemporaryFile() as f: ... nx.write_graph6(nx.path_graph(2), f.name) ... _ = f.seek(0) ... print(f.read()) b'>>graph6< """ return write_graph6_file(G, path, nodes=nodes, header=header) @not_implemented_for("directed") @not_implemented_for("multigraph") def write_graph6_file(G, f, nodes=None, header=True): """Write a simple undirected graph to a file-like object in graph6 format. Parameters ---------- G : Graph (undirected) f : file-like object The file to write. nodes: list or iterable Nodes are labeled 0...n-1 in the order provided. If None the ordering given by ``G.nodes()`` is used. header: bool If True add '>>graph6<<' string to head of data Raises ------ NetworkXNotImplemented If the graph is directed or is a multigraph. ValueError If the graph has at least ``2 ** 36`` nodes; the graph6 format is only defined for graphs of order less than ``2 ** 36``. Examples -------- You can write a graph6 file by giving an open file-like object:: >>> import tempfile >>> with tempfile.NamedTemporaryFile() as f: ... nx.write_graph6(nx.path_graph(2), f) ... _ = f.seek(0) ... print(f.read()) b'>>graph6< """ if nodes is not None: G = G.subgraph(nodes) H = nx.convert_node_labels_to_integers(G) nodes = sorted(H.nodes()) for b in _generate_graph6_bytes(H, nodes, header): f.write(b) def data_to_n(data): """Read initial one-, four- or eight-unit value from graph6 integer sequence. Return (value, rest of seq.)""" if data[0] <= 62: return data[0], data[1:] if data[1] <= 62: return (data[1] << 12) + (data[2] << 6) + data[3], data[4:] return ( (data[2] << 30) + (data[3] << 24) + (data[4] << 18) + (data[5] << 12) + (data[6] << 6) + data[7], data[8:], ) def n_to_data(n): """Convert an integer to one-, four- or eight-unit graph6 sequence. This function is undefined if `n` is not in ``range(2 ** 36)``. """ if n <= 62: return [n] elif n <= 258047: return [63, (n >> 12) & 0x3F, (n >> 6) & 0x3F, n & 0x3F] else: # if n <= 68719476735: return [ 63, 63, (n >> 30) & 0x3F, (n >> 24) & 0x3F, (n >> 18) & 0x3F, (n >> 12) & 0x3F, (n >> 6) & 0x3F, n & 0x3F, ]