def _single_source_dijkstra_path_basic(G, s, weight):
# modified from Eppstein
S = []
P = {}
for v in G:
P[v] = []
sigma = dict.fromkeys(G, 0.0) # sigma[v]=0 for v in G
D = {}
sigma[s] = 1.0
push = heappush
pop = heappop
seen = {s: 0}
c = count()
Q = [] # use Q as heap with (distance,node id) tuples
push(Q, (0, next(c), s, s))
while Q:
(dist, _, pred, v) = pop(Q)
if v in D:
continue # already searched this node.
sigma[v] += sigma[pred] # count paths
S.append(v)
D[v] = dist
for w, edgedata in G[v].items():
vw_dist = dist + edgedata.get(weight, 1)
if w not in D and (w not in seen or vw_dist < seen[w]):
seen[w] = vw_dist
push(Q, (vw_dist, next(c), v, w))
sigma[w] = 0.0
P[w] = [v]
elif vw_dist == seen[w]: # handle equal paths
sigma[w] += sigma[v]
P[w].append(v)
return S, P, sigma
def parseData():
"""Return stream of pairs b[i], x[i] for sparse6 format."""
chunks = iter(data)
d = None # partial data word
dLen = 0 # how many unparsed bits are left in d
while 1:
if dLen < 1:
try:
d = next(chunks)
except StopIteration:
return
dLen = 6
dLen -= 1
b = (d >> dLen) & 1 # grab top remaining bit
x = d & ((1 << dLen) - 1) # partially built up value of x
xLen = dLen # how many bits included so far in x
while xLen < k: # now grab full chunks until we have enough
try:
d = next(chunks)
except StopIteration:
return
dLen = 6
x = (x << 6) + d
xLen += 6
x = (x >> (xLen - k)) # shift back the extra bits
dLen = xLen - k
yield b, x
def parse_kv(curr_token):
dct = defaultdict(list)
while curr_token[0] == 0: # keys
key = curr_token[1]
curr_token = next(tokens)
category = curr_token[0]
if category == 1 or category == 2: # reals or ints
value = curr_token[1]
curr_token = next(tokens)
elif category == 3: # strings
value = unescape(curr_token[1][1:-1])
if destringizer:
try:
value = destringizer(value)
except ValueError:
pass
curr_token = next(tokens)
elif category == 4: # dict start
curr_token, value = parse_dict(curr_token)
else:
unexpected(curr_token, "an int, float, string or '['")
dct[key].append(value)
dct = dict((key, (value if not isinstance(value, list)
or len(value) != 1 else value[0]))
for key, value in dct.items())
return curr_token, dct
def test_shortest_simple_paths():
G = cnlti(nx.grid_2d_graph(4, 4), first_label=1, ordering="sorted")
paths = nx.shortest_simple_paths(G, 1, 12)
assert_equal(next(paths), [1, 2, 3, 4, 8, 12])
assert_equal(next(paths), [1, 5, 6, 7, 8, 12])
assert_equal([len(path) for path in nx.shortest_simple_paths(G, 1, 12)],
sorted([len(path) for path in nx.all_simple_paths(G, 1, 12)]))
def _alternating_dfs(u, along_matched=True):
"""Returns True if and only if `u` is connected to one of the
targets by an alternating path.
`u` is a vertex in the graph `G`.
If `along_matched` is True, this step of the depth-first search
will continue only through edges in the given matching. Otherwise, it
will continue only through edges *not* in the given matching.
"""
if along_matched:
edges = itertools.cycle([matched_edges, unmatched_edges])
else:
edges = itertools.cycle([unmatched_edges, matched_edges])
visited = set()
stack = [(u, iter(G[u]), next(edges))]
while stack:
parent, children, valid_edges = stack[-1]
try:
child = next(children)
if child not in visited:
if ((parent, child) in valid_edges
or (child, parent) in valid_edges):
if child in targets:
return True
visited.add(child)
stack.append((child, iter(G[child]), next(edges)))
except StopIteration:
stack.pop()
return False
def parse_p2g(lines):
"""Parse p2g format graph from string or iterable.
Returns
-------
MultiDiGraph
"""
description = next(lines).strip()
# are multiedges (parallel edges) allowed?
G = networkx.MultiDiGraph(name=description, selfloops=True)
nnodes, nedges = map(int, next(lines).split())
nodelabel = {}
nbrs = {}
# loop over the nodes keeping track of node labels and out neighbors
# defer adding edges until all node labels are known
for i in range(nnodes):
n = next(lines).strip()
nodelabel[i] = n
G.add_node(n)
nbrs[n] = map(int, next(lines).split())
# now we know all of the node labels so we can add the edges
# with the correct labels
for n in G:
for nbr in nbrs[n]:
G.add_edge(n, nodelabel[nbr])
return G
def has_bridges(G, root=None):
"""Decide whether a graph has any bridges.
A *bridge* in a graph is an edge whose removal causes the number of
connected components of the graph to increase.
Parameters
----------
G : undirected graph
root : node (optional)
A node in the graph `G`. If specified, only the bridges in the
connected component containing this node will be considered.
Returns
-------
bool
Whether the graph (or the connected component containing `root`)
has any bridges.
Raises
------
NodeNotFound
If `root` is not in the graph `G`.
Examples
--------
The barbell graph with parameter zero has a single bridge::
>>> G = nx.barbell_graph(10, 0)
>>> nx.has_bridges(G)
True
On the other hand, the cycle graph has no bridges::
>>> G = nx.cycle_graph(5)
>>> nx.has_bridges(G)
False
Notes
-----
This implementation uses the :func:`networkx.bridges` function, so
it shares its worst-case time complexity, $O(m + n)$, ignoring
polylogarithmic factors, where $n$ is the number of nodes in the
graph and $m$ is the number of edges.
"""
try:
next(bridges(G))
except StopIteration:
return False
else:
return True
def cycles(seq):
"""Yields cyclic permutations of the given sequence.
For example::
>>> list(cycles('abc'))
[('a', 'b', 'c'), ('b', 'c', 'a'), ('c', 'a', 'b')]
"""
n = len(seq)
cycled_seq = cycle(seq)
for x in seq:
yield tuple(islice(cycled_seq, n))
next(cycled_seq)
def check_counterexample(G, sub_graph):
"""Raises an exception if the counterexample is wrong.
Parameters
----------
G : NetworkX graph
subdivision_nodes : set
A set of nodes inducing a subgraph as a counterexample
"""
# 1. Create the sub graph
sub_graph = nx.Graph(sub_graph)
# 2. Remove self loops
for u in sub_graph:
if sub_graph.has_edge(u, u):
sub_graph.remove_edge(u, u)
# keep track of nodes we might need to contract
contract = list(sub_graph)
# 3. Contract Edges
while len(contract) > 0:
contract_node = contract.pop()
if contract_node not in sub_graph:
# Node was already contracted
continue
degree = sub_graph.degree[contract_node]
# Check if we can remove the node
if degree == 2:
# Get the two neighbors
neighbors = iter(sub_graph[contract_node])
u = next(neighbors)
v = next(neighbors)
# Save nodes for later
contract.append(u)
contract.append(v)
# Contract edge
sub_graph.remove_node(contract_node)
sub_graph.add_edge(u, v)
# 4. Check for isomorphism with K5 or K3_3 graphs
if len(sub_graph) == 5:
if not nx.is_isomorphic(nx.complete_graph(5), sub_graph):
raise nx.NetworkXException("Bad counter example.")
elif len(sub_graph) == 6:
if not nx.is_isomorphic(nx.complete_bipartite_graph(3, 3), sub_graph):
raise nx.NetworkXException("Bad counter example.")
else:
raise nx.NetworkXException("Bad counter example.")
def test_iter(self):
nv = self.nv
for i, n in enumerate(nv):
assert_equal(i, n)
inv = iter(nv)
assert_equal(next(inv), 0)
assert_not_equal(iter(nv), nv)
assert_equal(iter(inv), inv)
inv2 = iter(nv)
next(inv2)
assert_equal(list(inv), list(inv2))
# odd case where NodeView calls NodeDataView with data=False
nnv = nv(data=False)
for i, n in enumerate(nnv):
assert_equal(i, n)
def pairwise(iterable, cyclic=False):
"s -> (s0, s1), (s1, s2), (s2, s3), ..."
a, b = tee(iterable)
first = next(b, None)
if cyclic is True:
return zip(a, chain(b, (first, )))
return zip(a, b)
def arbitrary_element(iterable):
"""Returns an arbitrary element of `iterable` without removing it.
This is most useful for "peeking" at an arbitrary element of a set,
but can be used for any list, dictionary, etc., as well::
>>> arbitrary_element({3, 2, 1})
1
>>> arbitrary_element('hello')
'h'
This function raises a :exc:`ValueError` if `iterable` is an
iterator (because the current implementation of this function would
consume an element from the iterator)::
>>> iterator = iter([1, 2, 3])
>>> arbitrary_element(iterator)
Traceback (most recent call last):
...
ValueError: cannot return an arbitrary item from an iterator
"""
if is_iterator(iterable):
raise ValueError('cannot return an arbitrary item from an iterator')
# Another possible implementation is ``for x in iterable: return x``.
return next(iter(iterable))
def add_path(G_to_add_to, nodes_for_path, **attr):
"""Add a path to the Graph G_to_add_to.
Parameters
----------
G_to_add_to : graph
A NetworkX graph
nodes_for_path : iterable container
A container of nodes. A path will be constructed from
the nodes (in order) and added to the graph.
attr : keyword arguments, optional (default= no attributes)
Attributes to add to every edge in path.
See Also
--------
add_star, add_cycle
Examples
--------
>>> G = nx.Graph()
>>> nx.add_path(G, [0, 1, 2, 3])
>>> nx.add_path(G, [10, 11, 12], weight=7)
"""
nlist = iter(nodes_for_path)
try:
first_node = next(nlist)
except StopIteration:
return
G_to_add_to.add_node(first_node)
G_to_add_to.add_edges_from(pairwise(chain((first_node, ), nlist)), **attr)
def add_star(G_to_add_to, nodes_for_star, **attr):
"""Add a star to Graph G_to_add_to.
The first node in `nodes_for_star` is the middle of the star.
It is connected to all other nodes.
Parameters
----------
G_to_add_to : graph
A NetworkX graph
nodes_for_star : iterable container
A container of nodes.
attr : keyword arguments, optional (default= no attributes)
Attributes to add to every edge in star.
See Also
--------
add_path, add_cycle
Examples
--------
>>> G = nx.Graph()
>>> nx.add_star(G, [0, 1, 2, 3])
>>> nx.add_star(G, [10, 11, 12], weight=2)
"""
nlist = iter(nodes_for_star)
v = next(nlist)
edges = ((v, n) for n in nlist)
G_to_add_to.add_edges_from(edges, **attr)
def subgraph_is_isomorphic(self):
"""Returns True if a subgraph of G1 is isomorphic to G2."""
try:
x = next(self.subgraph_isomorphisms_iter())
return True
except StopIteration:
return False
def test_iter(self):
nv = self.nv
for i, (n, d) in enumerate(nv):
assert_equal(i, n)
assert_equal(d, {})
inv = iter(nv)
assert_equal(next(inv), (0, {}))
self.G.nodes[3]['foo'] = 'bar'
# default
for n, d in nv:
if n == 3:
assert_equal(d, {'foo': 'bar'})
else:
assert_equal(d, {})
# data=True
for n, d in self.ndv:
if n == 3:
assert_equal(d, {'foo': 'bar'})
else:
assert_equal(d, {})
# data='foo'
for n, d in self.nwv:
if n == 3:
assert_equal(d, 'bar')
else:
assert_equal(d, None)
# data='foo', default=1
for n, d in self.G.nodes.data('foo', default=1):
if n == 3:
assert_equal(d, 'bar')
else:
assert_equal(d, 1)
def get_attr_id(self, title, attr_type, edge_or_node, default, mode):
# find the id of the attribute or generate a new id
try:
return self.attr[edge_or_node][mode][title]
except KeyError:
# generate new id
new_id = str(next(self.attr_id))
self.attr[edge_or_node][mode][title] = new_id
attr_kwargs = {'id': new_id, 'title': title, 'type': attr_type}
attribute = Element('attribute', **attr_kwargs)
# add subelement for data default value if present
default_title = default.get(title)
if default_title is not None:
default_element = Element('default')
default_element.text = make_str(default_title)
attribute.append(default_element)
# new insert it into the XML
attributes_element = None
for a in self.graph_element.findall('attributes'):
# find existing attributes element by class and mode
a_class = a.get('class')
a_mode = a.get('mode', 'static')
if a_class == edge_or_node and a_mode == mode:
attributes_element = a
if attributes_element is None:
# create new attributes element
attr_kwargs = {'mode': mode, 'class': edge_or_node}
attributes_element = Element('attributes', **attr_kwargs)
self.graph_element.insert(0, attributes_element)
attributes_element.append(attribute)
return new_id
def disjoint_union_all(graphs):
"""Return the disjoint union of all graphs.
This operation forces distinct integer node labels starting with 0
for the first graph in the list and numbering consecutively.
Parameters
----------
graphs : list
List of NetworkX graphs
Returns
-------
U : A graph with the same type as the first graph in list
Raises
------
ValueError
If `graphs` is an empty list.
Notes
-----
It is recommended that the graphs be either all directed or all undirected.
Graph, edge, and node attributes are propagated to the union graph.
If a graph attribute is present in multiple graphs, then the value
from the last graph in the list with that attribute is used.
"""
if not graphs:
raise ValueError('cannot apply disjoint_union_all to an empty list')
graphs = iter(graphs)
U = next(graphs)
for H in graphs:
U = nx.disjoint_union(U, H)
return U
def test_articulation_points():
Ggen = _generate_no_biconnected()
for i in range(1): # change 1 to 3 or more for more realizations.
G = next(Ggen)
articulation_points = list(set([a]) for a in nx.articulation_points(G))
for cut in nx.all_node_cuts(G):
assert_true(cut in articulation_points)
def test_no_weight(self):
inf = float('inf')
expected = set([(3, 4, inf), (4, 3, inf)])
assert_in(next(nx.local_bridges(self.BB)), expected)
expected = set([(u, v, 3) for u, v, in self.square.edges])
assert_equal(set(nx.local_bridges(self.square)), expected)
assert_equal(list(nx.local_bridges(self.tri)), [])
def intersection_all(graphs):
"""Return a new graph that contains only the edges that exist in
all graphs.
All supplied graphs must have the same node set.
Parameters
----------
graphs : list
List of NetworkX graphs
Returns
-------
R : A new graph with the same type as the first graph in list
Raises
------
ValueError
If `graphs` is an empty list.
Notes
-----
Attributes from the graph, nodes, and edges are not copied to the new
graph.
"""
if not graphs:
raise ValueError('cannot apply intersection_all to an empty list')
graphs = iter(graphs)
R = next(graphs)
for H in graphs:
R = nx.intersection(R, H)
return R
def _tree_edges(n, r):
if n == 0:
return
# helper function for trees
# yields edges in rooted tree at 0 with n nodes and branching ratio r
nodes = iter(range(n))
parents = [next(nodes)] # stack of max length r
while parents:
source = parents.pop(0)
for i in range(r):
try:
target = next(nodes)
parents.append(target)
yield source, target
except StopIteration:
break
def edge_key_data(G):
# helper function to unify multigraph and graph edge iterator
if G.is_multigraph():
for u, v, key, data in G.edges(data=True, keys=True):
edge_data = data.copy()
edge_data.update(key=key)
edge_id = edge_data.pop('id', None)
if edge_id is None:
edge_id = next(self.edge_id)
yield u, v, edge_id, edge_data
else:
for u, v, data in G.edges(data=True):
edge_data = data.copy()
edge_id = edge_data.pop('id', None)
if edge_id is None:
edge_id = next(self.edge_id)
yield u, v, edge_id, edge_data
def insert(self, key, value, allow_increase=False):
dict = self._dict
if key in dict:
old_value = dict[key]
if value < old_value or (allow_increase and value > old_value):
# Since there is no way to efficiently obtain the location of a
# key-value pair in the heap, insert a new pair even if ones
# with the same key may already be present. Deem the old ones
# as stale and skip them when the minimum pair is queried.
dict[key] = value
heappush(self._heap, (value, next(self._count), key))
return value < old_value
return False
else:
dict[key] = value
heappush(self._heap, (value, next(self._count), key))
return True
def test_articulation_points():
Ggen = _generate_no_biconnected()
for flow_func in flow_funcs:
for i in range(3):
G = next(Ggen)
assert_equal(nx.node_connectivity(G, flow_func=flow_func),
1,
msg=msg % (flow_func.__name__, ))
def suitable_edge(self):
"""Returns True if and only if an arbitrary remaining node can
potentially be joined with some other remaining node.
"""
nodes = iter(self.remaining_degree)
u = next(nodes)
return any(v not in self.graph[u] for v in nodes)
def test_iter(self):
ev = self.eview(self.G)
for u, v, k in ev:
pass
iev = iter(ev)
assert_equal(next(iev), (0, 1, 0))
assert_not_equal(iter(ev), ev)
assert_equal(iter(iev), iev)
def test_iter(self):
dv = self.dview(self.G)
for n, d in dv:
pass
idv = iter(dv)
assert_not_equal(iter(dv), dv)
assert_equal(iter(idv), idv)
assert_equal(next(idv), (0, dv[0]))
assert_equal(next(idv), (1, dv[1]))
# weighted
dv = self.dview(self.G, weight='foo')
for n, d in dv:
pass
idv = iter(dv)
assert_not_equal(iter(dv), dv)
assert_equal(iter(idv), idv)
assert_equal(next(idv), (0, dv[0]))
assert_equal(next(idv), (1, dv[1]))
def test_iter(self):
evr = self.eview(self.G)
ev = evr()
for u, v in ev:
pass
iev = iter(ev)
assert_equal(next(iev), (0, 1))
assert_not_equal(iter(ev), ev)
assert_equal(iter(iev), iev)
def test_articulation_points():
Ggen = _generate_no_biconnected()
for flow_func in flow_funcs:
for i in range(1): # change 1 to 3 or more for more realizations.
G = next(Ggen)
cut = nx.minimum_node_cut(G, flow_func=flow_func)
assert_true(len(cut) == 1, msg=msg % (flow_func.__name__, ))
assert_true(cut.pop() in set(nx.articulation_points(G)),
msg=msg % (flow_func.__name__, ))
