def test_small_graph_centrality(self):
G = nx.empty_graph(create_using=nx.DiGraph)
assert {} == nx.degree_centrality(G)
assert {} == nx.out_degree_centrality(G)
assert {} == nx.in_degree_centrality(G)
G = nx.empty_graph(1, create_using=nx.DiGraph)
assert {0: 1} == nx.degree_centrality(G)
assert {0: 1} == nx.out_degree_centrality(G)
assert {0: 1} == nx.in_degree_centrality(G)
def parse_adjlist(lines,
comments="#",
delimiter=None,
create_using=None,
nodetype=None):
G = nx.empty_graph(0, create_using)
edges = []
for line in lines:
p = line.find(comments)
if p >= 0:
line = line[:p]
if not len(line):
continue
vlist = line.strip().split(delimiter)
u = vlist.pop(0)
# convert types
if nodetype is not None:
try:
u = nodetype(u)
except Exception as e:
raise TypeError(
"Failed to convert node ({}) to type {}".format(
u, nodetype)) from e
if nodetype is not None:
try:
vlist = map(nodetype, vlist)
except Exception as e:
raise TypeError(
"Failed to convert nodes ({}) to type {}".format(
",".join(vlist), nodetype)) from e
edges.extend([u, v] for v in vlist)
G.add_edges_from(edges)
return G
def from_pandas_edgelist(df,
source="source",
target="target",
edge_attr=None,
create_using=None):
g = nx.empty_graph(0, create_using)
if edge_attr is None:
g.add_edges_from(zip(df[source], df[target]))
return g
# Additional columns requested
if edge_attr is True:
cols = [c for c in df.columns if c is not source and c is not target]
elif isinstance(edge_attr, (list, tuple)):
cols = edge_attr
else:
cols = [edge_attr]
if len(cols) == 0:
msg = f"Invalid edge_attr argument. No columns found with name: {cols}"
raise nx.NetworkXError(msg)
try:
eattrs = zip(*[df[col] for col in cols])
except (KeyError, TypeError) as e:
msg = f"Invalid edge_attr argument: {edge_attr}"
raise nx.NetworkXError(msg) from e
edges = []
for s, t, attrs in zip(df[source], df[target], eattrs):
edges.append((s, t, zip(cols, attrs)))
g.add_edges_from(edges)
return g
def parse_edgelist(
lines, comments="#", delimiter=None, create_using=None, nodetype=None, data=True
):
from ast import literal_eval
G = nx.empty_graph(0, create_using)
edges = []
for line in lines:
p = line.find(comments)
if p >= 0:
line = line[:p]
if not len(line):
continue
# split line, should have 2 or more
s = line.strip().split(delimiter)
if len(s) < 2:
continue
u = s.pop(0)
v = s.pop(0)
d = s
if nodetype is not None:
try:
u = nodetype(u)
v = nodetype(v)
except Exception as e:
raise TypeError(
"Failed to convert nodes %s,%s to type %s." % (u, v, nodetype)
) from e
if len(d) == 0 or data is False:
# no data or data type specified
edgedata = {}
elif data is True:
# no edge types specified
try: # try to evaluate as dictionary
edgedata = dict(literal_eval(" ".join(d)))
except Exception as e:
raise TypeError(
"Failed to convert edge data (%s) to dictionary." % (d)
) from e
else:
# convert edge data to dictionary with specified keys and type
if len(d) != len(data):
raise IndexError(
"Edge data %s and data_keys %s are not the same length" % (d, data)
)
edgedata = {}
for (edge_key, edge_type), edge_value in zip(data, d):
try:
edge_value = edge_type(edge_value)
except Exception as e:
raise TypeError(
"Failed to convert %s data %s to type %s."
% (edge_key, edge_value, edge_type)
) from e
edgedata.update({edge_key: edge_value})
edges.append((u, v, edgedata))
G.add_edges_from(edges)
return G
def binomial_tree(n):
G = nx.empty_graph(1)
N = 1
for i in range(n):
edges = [(u + N, v + N) for (u, v) in G.edges]
G.add_edges_from(edges)
G.add_edge(0, N)
N *= 2
return G
def random_k_out_graph(n, k, alpha, self_loops=True, seed=None):
"""Returns a random `k`-out graph with preferential attachment.
A random `k`-out graph with preferential attachment is a
multidigraph generated by the following algorithm.
1. Begin with an empty digraph, and initially set each node to have
weight `alpha`.
2. Choose a node `u` with out-degree less than `k` uniformly at
random.
3. Choose a node `v` from with probability proportional to its
weight.
4. Add a directed edge from `u` to `v`, and increase the weight
of `v` by one.
5. If each node has out-degree `k`, halt, otherwise repeat from
step 2.
For more information on this model of random graph, see [1].
Parameters
----------
n : int
The number of nodes in the returned graph.
k : int
The out-degree of each node in the returned graph.
alpha : float
A positive :class:`float` representing the initial weight of
each vertex. A higher number means that in step 3 above, nodes
will be chosen more like a true uniformly random sample, and a
lower number means that nodes are more likely to be chosen as
their in-degree increases. If this parameter is not positive, a
:exc:`ValueError` is raised.
self_loops : bool
If True, self-loops are allowed when generating the graph.
seed : integer, random_state, or None (default)
Indicator of random number generation state.
See :ref:`Randomness<randomness>`.
Returns
-------
:class:`~networkx.classes.MultiDiGraph`
A `k`-out-regular multidigraph generated according to the above
algorithm.
Raises
------
ValueError
If `alpha` is not positive.
Notes
-----
The returned multidigraph may not be strongly connected, or even
weakly connected.
References
----------
[1]: Peterson, Nicholas R., and Boris Pittel.
"Distance between two random `k`-out digraphs, with and without
preferential attachment."
arXiv preprint arXiv:1311.5961 (2013).
<https://arxiv.org/abs/1311.5961>
"""
if alpha < 0:
raise ValueError("alpha must be positive")
G = nx.empty_graph(n, create_using=nx.MultiDiGraph)
weights = Counter({v: alpha for v in G})
for i in range(k * n):
u = seed.choice([v for v, d in G.out_degree() if d < k])
# If self-loops are not allowed, make the source node `u` have
# weight zero.
if not self_loops:
adjustment = Counter({u: weights[u]})
else:
adjustment = Counter()
v = weighted_choice(weights - adjustment, seed=seed)
G.add_edge(u, v)
weights[v] += 1
return G
def random_uniform_k_out_graph(n, k, self_loops=True, with_replacement=True, seed=None):
"""Returns a random `k`-out graph with uniform attachment.
A random `k`-out graph with uniform attachment is a multidigraph
generated by the following algorithm. For each node *u*, choose
`k` nodes *v* uniformly at random (with replacement). Add a
directed edge joining *u* to *v*.
Parameters
----------
n : int
The number of nodes in the returned graph.
k : int
The out-degree of each node in the returned graph.
self_loops : bool
If True, self-loops are allowed when generating the graph.
with_replacement : bool
If True, neighbors are chosen with replacement and the
returned graph will be a directed multigraph. Otherwise,
neighbors are chosen without replacement and the returned graph
will be a directed graph.
seed : integer, random_state, or None (default)
Indicator of random number generation state.
See :ref:`Randomness<randomness>`.
Returns
-------
NetworkX graph
A `k`-out-regular directed graph generated according to the
above algorithm. It will be a multigraph if and only if
`with_replacement` is True.
Raises
------
ValueError
If `with_replacement` is False and `k` is greater than
`n`.
See also
--------
random_k_out_graph
Notes
-----
The return digraph or multidigraph may not be strongly connected, or
even weakly connected.
If `with_replacement` is True, this function is similar to
:func:`random_k_out_graph`, if that function had parameter `alpha`
set to positive infinity.
"""
if with_replacement:
create_using = nx.MultiDiGraph()
def sample(v, nodes):
if not self_loops:
nodes = nodes - {v}
return (seed.choice(list(nodes)) for i in range(k))
else:
create_using = nx.DiGraph()
def sample(v, nodes):
if not self_loops:
nodes = nodes - {v}
return seed.sample(nodes, k)
G = nx.empty_graph(n, create_using)
nodes = set(G)
for u in G:
G.add_edges_from((u, v) for v in sample(u, nodes))
return G
def scale_free_graph(
n,
alpha=0.41,
beta=0.54,
gamma=0.05,
delta_in=0.2,
delta_out=0,
create_using=None,
seed=None,
):
"""Returns a scale-free directed graph.
Parameters
----------
n : integer
Number of nodes in graph
alpha : float
Probability for adding a new node connected to an existing node
chosen randomly according to the in-degree distribution.
beta : float
Probability for adding an edge between two existing nodes.
One existing node is chosen randomly according the in-degree
distribution and the other chosen randomly according to the out-degree
distribution.
gamma : float
Probability for adding a new node connected to an existing node
chosen randomly according to the out-degree distribution.
delta_in : float
Bias for choosing nodes from in-degree distribution.
delta_out : float
Bias for choosing nodes from out-degree distribution.
create_using : NetworkX graph constructor, optional
The default is a MultiDiGraph 3-cycle.
If a graph instance, use it without clearing first.
If a graph constructor, call it to construct an empty graph.
seed : integer, random_state, or None (default)
Indicator of random number generation state.
See :ref:`Randomness<randomness>`.
Examples
--------
Create a scale-free graph on one hundred nodes::
>>> G = nx.scale_free_graph(100)
Notes
-----
The sum of `alpha`, `beta`, and `gamma` must be 1.
References
----------
.. [1] B. Bollobás, C. Borgs, J. Chayes, and O. Riordan,
Directed scale-free graphs,
Proceedings of the fourteenth annual ACM-SIAM Symposium on
Discrete Algorithms, 132--139, 2003.
"""
def _choose_node(G, distribution, delta, psum):
cumsum = 0.0
# normalization
r = seed.random()
for n, d in distribution:
cumsum += (d + delta) / psum
if r < cumsum:
break
return n
if create_using is None or not hasattr(create_using, "_adj"):
# start with 3-cycle
G = nx.empty_graph(3, create_using, default=nx.MultiDiGraph)
G.add_edges_from([(0, 1), (1, 2), (2, 0)])
else:
G = create_using
if not (G.is_directed() and G.is_multigraph()):
raise nx.NetworkXError("MultiDiGraph required in create_using")
if alpha <= 0:
raise ValueError("alpha must be > 0.")
if beta <= 0:
raise ValueError("beta must be > 0.")
if gamma <= 0:
raise ValueError("gamma must be > 0.")
if abs(alpha + beta + gamma - 1.0) >= 1e-9:
raise ValueError("alpha+beta+gamma must equal 1.")
number_of_edges = G.number_of_edges()
while len(G) < n:
psum_in = number_of_edges + delta_in * len(G)
psum_out = number_of_edges + delta_out * len(G)
r = seed.random()
# random choice in alpha,beta,gamma ranges
if r < alpha:
# alpha
# add new node v
v = len(G)
# choose w according to in-degree and delta_in
w = _choose_node(G, G.in_degree(), delta_in, psum_in)
elif r < alpha + beta:
# beta
# choose v according to out-degree and delta_out
v = _choose_node(G, G.out_degree(), delta_out, psum_out)
# choose w according to in-degree and delta_in
w = _choose_node(G, G.in_degree(), delta_in, psum_in)
else:
# gamma
# choose v according to out-degree and delta_out
v = _choose_node(G, G.out_degree(), delta_out, psum_out)
# add new node w
w = len(G)
G.add_edge(v, w)
number_of_edges += 1
return G