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| # 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 not_implemented_for, open_file | |
| __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 | |
| <http://users.cecs.anu.edu.au/~bdm/data/formats.html> | |
| """ | |
| 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<<A_\\n' | |
| See Also | |
| -------- | |
| from_graph6_bytes, read_graph6, write_graph6_bytes | |
| Notes | |
| ----- | |
| The returned bytes end with a newline character. | |
| The format does not support edge or node labels, parallel edges or | |
| self loops. If self loops are present they are silently ignored. | |
| References | |
| ---------- | |
| .. [1] Graph6 specification | |
| <http://users.cecs.anu.edu.au/~bdm/data/formats.html> | |
| """ | |
| 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)) | |
| 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(delete=False) as f: | |
| ... _ = f.write(b">>graph6<<A_\\n") | |
| ... _ = f.seek(0) | |
| ... G = nx.read_graph6(f.name) | |
| >>> 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<<A_\\n") | |
| ... _ = f.seek(0) | |
| ... G = nx.read_graph6(f) | |
| >>> list(G.edges()) | |
| [(0, 1)] | |
| See Also | |
| -------- | |
| from_graph6_bytes, write_graph6 | |
| References | |
| ---------- | |
| .. [1] Graph6 specification | |
| <http://users.cecs.anu.edu.au/~bdm/data/formats.html> | |
| """ | |
| 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 | |
| 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(delete=False) as f: | |
| ... nx.write_graph6(nx.path_graph(2), f.name) | |
| ... _ = f.seek(0) | |
| ... print(f.read()) | |
| b'>>graph6<<A_\\n' | |
| See Also | |
| -------- | |
| from_graph6_bytes, read_graph6 | |
| Notes | |
| ----- | |
| The function writes a newline character after writing the encoding | |
| of the graph. | |
| The format does not support edge or node labels, parallel edges or | |
| self loops. If self loops are present they are silently ignored. | |
| References | |
| ---------- | |
| .. [1] Graph6 specification | |
| <http://users.cecs.anu.edu.au/~bdm/data/formats.html> | |
| """ | |
| return write_graph6_file(G, path, nodes=nodes, header=header) | |
| 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<<A_\\n' | |
| See Also | |
| -------- | |
| from_graph6_bytes, read_graph6 | |
| Notes | |
| ----- | |
| The function writes a newline character after writing the encoding | |
| of the graph. | |
| The format does not support edge or node labels, parallel edges or | |
| self loops. If self loops are present they are silently ignored. | |
| References | |
| ---------- | |
| .. [1] Graph6 specification | |
| <http://users.cecs.anu.edu.au/~bdm/data/formats.html> | |
| """ | |
| 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, | |
| ] | |