def _generate_sparse6_bytes(G, nodes, header):
"""Yield bytes in the sparse6 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'>>sparse6<<'`` 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('sparse6 is only defined if number of nodes is less '
'than 2 ** 36')
if header:
yield b'>>sparse6<<'
yield b':'
for d in n_to_data(n):
yield str.encode(chr(d + 63))
k = 1
while 1 << k < n:
k += 1
def enc(x):
"""Big endian k-bit encoding of x"""
return [1 if (x & 1 << (k - 1 - i)) else 0 for i in range(k)]
edges = sorted((max(u, v), min(u, v)) for u, v in G.edges())
bits = []
curv = 0
for (v, u) in edges:
if v == curv: # current vertex edge
bits.append(0)
bits.extend(enc(u))
elif v == curv + 1: # next vertex edge
curv += 1
bits.append(1)
bits.extend(enc(u))
else: # skip to vertex v and then add edge to u
curv = v
bits.append(1)
bits.extend(enc(v))
bits.append(0)
bits.extend(enc(u))
if k < 6 and n == (1 << k) and ((-len(bits)) % 6) >= k and curv < (n - 1):
# Padding special case: small k, n=2^k,
# more than k bits of padding needed,
# current vertex is not (n-1) --
# appending 1111... would add a loop on (n-1)
bits.append(0)
bits.extend([1] * ((-len(bits)) % 6))
else:
bits.extend([1] * ((-len(bits)) % 6))
data = [(bits[i + 0] << 5) + (bits[i + 1] << 4) + (bits[i + 2] << 3) + (bits[i + 3] << 2) +
(bits[i + 4] << 1) + (bits[i + 5] << 0) for i in range(0, len(bits), 6)]
for d in data:
yield str.encode(chr(d + 63))
yield b'\n'
def generate_sparse6(G, nodes=None, header=True):
"""Generate sparse6 format string from an undirected graph.
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 '>>sparse6<<' string to head of data
Returns
-------
s : string
String in sparse6 format
Raises
------
NetworkXError
If the graph is directed
Examples
--------
>>> G = nx.MultiGraph([(0, 1), (0, 1), (0, 1)])
>>> nx.generate_sparse6(G)
'>>sparse6<<:A_'
See Also
--------
read_sparse6, parse_sparse6, write_sparse6
Notes
-----
The format does not support edge or node labels.
References
----------
Sparse6 specification:
http://cs.anu.edu.au/~bdm/data/formats.txt for details.
"""
n = G.order()
k = 1
while 1 << k < n:
k += 1
def enc(x):
"""Big endian k-bit encoding of x"""
return [1 if (x & 1 << (k - 1 - i)) else 0 for i in range(k)]
if nodes is None:
ns = list(G.nodes()) # number -> node
else:
ns = list(nodes)
ndict = dict(((ns[i], i) for i in range(len(ns)))) # node -> number
edges = [(ndict[u], ndict[v]) for (u, v) in G.edges()]
edges = [(max(u, v), min(u, v)) for (u, v) in edges]
edges.sort()
bits = []
curv = 0
for (v, u) in edges:
if v == curv: # current vertex edge
bits.append(0)
bits.extend(enc(u))
elif v == curv + 1: # next vertex edge
curv += 1
bits.append(1)
bits.extend(enc(u))
else: # skip to vertex v and then add edge to u
curv = v
bits.append(1)
bits.extend(enc(v))
bits.append(0)
bits.extend(enc(u))
if k < 6 and n == (1 << k) and ((-len(bits)) % 6) >= k and curv < (n - 1):
# Padding special case: small k, n=2^k,
# more than k bits of padding needed,
# current vertex is not (n-1) --
# appending 1111... would add a loop on (n-1)
bits.append(0)
bits.extend([1] * ((-len(bits)) % 6))
else:
bits.extend([1] * ((-len(bits)) % 6))
data = [(bits[i + 0] << 5) + (bits[i + 1] << 4) + (bits[i + 2] << 3) +
(bits[i + 3] << 2) + (bits[i + 4] << 1) + (bits[i + 5] << 0)
for i in range(0, len(bits), 6)]
res = (':' + data_to_graph6(n_to_data(n)) + data_to_graph6(data))
if header:
return '>>sparse6<<' + res
else:
return res
def test_n_data_n_conversion(self):
for i in [0, 1, 42, 62, 63, 64, 258047, 258048, 7744773, 68719476735]:
assert_equal(g6.data_to_n(g6.n_to_data(i))[0], i)
assert_equal(g6.data_to_n(g6.n_to_data(i))[1], [])
assert_equal(g6.data_to_n(g6.n_to_data(i) + [42, 43])[1], [42, 43])
def test_n_data_n_conversion(self):
for i in [0, 1, 42, 62, 63, 64, 258047, 258048, 7744773, 68719476735]:
assert g6.data_to_n(g6.n_to_data(i))[0] == i
assert g6.data_to_n(g6.n_to_data(i))[1] == []
assert g6.data_to_n(g6.n_to_data(i) + [42, 43])[1] == [42, 43]
def generate_sparse6(G, nodes=None, header=True):
"""Generate sparse6 format string from an undirected graph.
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 '>>sparse6<<' string to head of data
Returns
-------
s : string
String in sparse6 format
Raises
------
NetworkXError
If the graph is directed
Examples
--------
>>> G = nx.MultiGraph([(0, 1), (0, 1), (0, 1)])
>>> nx.generate_sparse6(G)
'>>sparse6<<:A_'
See Also
--------
read_sparse6, parse_sparse6, write_sparse6
Notes
-----
The format does not support edge or node labels.
References
----------
Sparse6 specification:
http://cs.anu.edu.au/~bdm/data/formats.txt for details.
"""
n = G.order()
k = 1
while 1<<k < n:
k += 1
def enc(x):
"""Big endian k-bit encoding of x"""
return [1 if (x & 1 << (k-1-i)) else 0 for i in range(k)]
if nodes is None:
ns = list(G.nodes()) # number -> node
else:
ns = list(nodes)
ndict = dict(((ns[i], i) for i in range(len(ns)))) # node -> number
edges = [(ndict[u], ndict[v]) for (u, v) in G.edges()]
edges = [(max(u,v), min(u,v)) for (u, v) in edges]
edges.sort()
bits = []
curv = 0
for (v, u) in edges:
if v == curv: # current vertex edge
bits.append(0)
bits.extend(enc(u))
elif v == curv + 1: # next vertex edge
curv += 1
bits.append(1)
bits.extend(enc(u))
else: # skip to vertex v and then add edge to u
curv = v
bits.append(1)
bits.extend(enc(v))
bits.append(0)
bits.extend(enc(u))
if k < 6 and n == (1 << k) and ((-len(bits)) % 6) >= k and curv < (n - 1):
# Padding special case: small k, n=2^k,
# more than k bits of padding needed,
# current vertex is not (n-1) --
# appending 1111... would add a loop on (n-1)
bits.append(0)
bits.extend([1] * ((-len(bits)) % 6))
else:
bits.extend([1] * ((-len(bits)) % 6))
data = [(bits[i+0]<<5) + (bits[i+1]<<4) + (bits[i+2]<<3) + (bits[i+3]<<2) +
(bits[i+4]<<1) + (bits[i+5]<<0) for i in range(0, len(bits), 6)]
res = (':' + data_to_graph6(n_to_data(n)) +
data_to_graph6(data))
if header:
return '>>sparse6<<' + res
else:
return res
def _generate_sparse6_bytes(G, nodes, header):
"""Yield bytes in the sparse6 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'>>sparse6<<'`` 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('sparse6 is only defined if number of nodes is less '
'than 2 ** 36')
if header:
yield b'>>sparse6<<'
yield b':'
for d in n_to_data(n):
yield str.encode(chr(d + 63))
k = 1
while 1<<k < n:
k += 1
def enc(x):
"""Big endian k-bit encoding of x"""
return [1 if (x & 1 << (k-1-i)) else 0 for i in range(k)]
edges = sorted((max(u, v), min(u, v)) for u, v in G.edges())
bits = []
curv = 0
for (v, u) in edges:
if v == curv: # current vertex edge
bits.append(0)
bits.extend(enc(u))
elif v == curv + 1: # next vertex edge
curv += 1
bits.append(1)
bits.extend(enc(u))
else: # skip to vertex v and then add edge to u
curv = v
bits.append(1)
bits.extend(enc(v))
bits.append(0)
bits.extend(enc(u))
if k < 6 and n == (1 << k) and ((-len(bits)) % 6) >= k and curv < (n - 1):
# Padding special case: small k, n=2^k,
# more than k bits of padding needed,
# current vertex is not (n-1) --
# appending 1111... would add a loop on (n-1)
bits.append(0)
bits.extend([1] * ((-len(bits)) % 6))
else:
bits.extend([1] * ((-len(bits)) % 6))
data = [(bits[i+0]<<5) + (bits[i+1]<<4) + (bits[i+2]<<3) + (bits[i+3]<<2) +
(bits[i+4]<<1) + (bits[i+5]<<0) for i in range(0, len(bits), 6)]
for d in data:
yield str.encode(chr(d + 63))
yield b'\n'
def test_n_data_n_conversion(self):
for i in [0, 1, 42, 62, 63, 64, 258047, 258048, 7744773, 68719476735]:
assert_equal(g6.data_to_n(g6.n_to_data(i))[0], i)
assert_equal(g6.data_to_n(g6.n_to_data(i))[1], [])
assert_equal(g6.data_to_n(g6.n_to_data(i) + [42, 43])[1],
[42, 43])
