def RandomGNP(n, p, seed=None, fast=True, method='Sage'):
r"""
Returns a random graph on `n` nodes. Each edge is inserted independently
with probability `p`.
INPUTS:
- ``n`` -- number of nodes of the digraph
- ``p`` -- probability of an edge
- ``seed`` -- integer seed for random number generator (default=None).
- ``fast`` -- boolean set to True (default) to use the algorithm with
time complexity in `O(n+m)` proposed in [3]_. It is designed for
generating large sparse graphs. It is faster than other methods for
*LARGE* instances (try it to know whether it is useful for you).
- ``method`` -- By default (```method='Sage'``), this function uses the
method implemented in ```sage.graphs.graph_generators_pyx.pyx``. When
``method='networkx'``, this function calls the NetworkX function
``fast_gnp_random_graph``, unless ``fast=False``, then
``gnp_random_graph``. Try them to know which method is the best for
you. The ``fast`` parameter is not taken into account by the 'Sage'
method so far.
REFERENCES:
.. [1] P. Erdos and A. Renyi. On Random Graphs, Publ. Math. 6, 290 (1959).
.. [2] E. N. Gilbert. Random Graphs, Ann. Math. Stat., 30, 1141 (1959).
.. [3] V. Batagelj and U. Brandes. Efficient generation of large
random networks. Phys. Rev. E, 71, 036113, 2005.
PLOTTING: When plotting, this graph will use the default spring-layout
algorithm, unless a position dictionary is specified.
EXAMPLES: We show the edge list of a random graph on 6 nodes with
probability `p = .4`::
sage: set_random_seed(0)
sage: graphs.RandomGNP(6, .4).edges(labels=False)
[(0, 1), (0, 5), (1, 2), (2, 4), (3, 4), (3, 5), (4, 5)]
We plot a random graph on 12 nodes with probability
`p = .71`::
sage: gnp = graphs.RandomGNP(12,.71)
sage: gnp.show() # long time
We view many random graphs using a graphics array::
sage: g = []
sage: j = []
sage: for i in range(9):
... k = graphs.RandomGNP(i+3,.43)
... g.append(k)
...
sage: for i in range(3):
... n = []
... for m in range(3):
... n.append(g[3*i + m].plot(vertex_size=50, vertex_labels=False))
... j.append(n)
...
sage: G = sage.plot.graphics.GraphicsArray(j)
sage: G.show() # long time
sage: graphs.RandomGNP(4,1)
Complete graph: Graph on 4 vertices
TESTS::
sage: graphs.RandomGNP(50,.2,method=50)
Traceback (most recent call last):
...
ValueError: 'method' must be equal to 'networkx' or to 'Sage'.
sage: set_random_seed(0)
sage: graphs.RandomGNP(50,.2, method="Sage").size()
243
sage: graphs.RandomGNP(50,.2, method="networkx").size()
258
"""
if n < 0:
raise ValueError("The number of nodes must be positive or null.")
if 0.0 > p or 1.0 < p:
raise ValueError("The probability p must be in [0..1].")
if seed is None:
seed = current_randstate().long_seed()
if p == 1:
from sage.graphs.generators.basic import CompleteGraph
return CompleteGraph(n)
if method == 'networkx':
import networkx
if fast:
G = networkx.fast_gnp_random_graph(n, p, seed=seed)
else:
G = networkx.gnp_random_graph(n, p, seed=seed)
return graph.Graph(G)
elif method in ['Sage', 'sage']:
# We use the Sage generator
from sage.graphs.graph_generators_pyx import RandomGNP as sageGNP
return sageGNP(n, p)
else:
raise ValueError("'method' must be equal to 'networkx' or to 'Sage'.")
def RandomGNP(n, p, seed=None, fast=True, method='Sage'):
r"""
Returns a random graph on `n` nodes. Each edge is inserted independently
with probability `p`.
INPUTS:
- ``n`` -- number of nodes of the graph
- ``p`` -- probability of an edge
- ``seed`` -- integer seed for random number generator (default=None).
- ``fast`` -- boolean set to True (default) to use the algorithm with
time complexity in `O(n+m)` proposed in [BatBra2005]_. It is designed
for generating large sparse graphs. It is faster than other methods for
*LARGE* instances (try it to know whether it is useful for you).
- ``method`` -- By default (```method='Sage'``), this function uses the
method implemented in ```sage.graphs.graph_generators_pyx.pyx``. When
``method='networkx'``, this function calls the NetworkX function
``fast_gnp_random_graph``, unless ``fast=False``, then
``gnp_random_graph``. Try them to know which method is the best for
you. The ``fast`` parameter is not taken into account by the 'Sage'
method so far.
REFERENCES:
.. [ErdRen1959] P. Erdos and A. Renyi. On Random Graphs, Publ.
Math. 6, 290 (1959).
.. [Gilbert1959] E. N. Gilbert. Random Graphs, Ann. Math. Stat.,
30, 1141 (1959).
.. [BatBra2005] V. Batagelj and U. Brandes. Efficient generation of
large random networks. Phys. Rev. E, 71, 036113, 2005.
PLOTTING: When plotting, this graph will use the default spring-layout
algorithm, unless a position dictionary is specified.
EXAMPLES: We show the edge list of a random graph on 6 nodes with
probability `p = .4`::
sage: set_random_seed(0)
sage: graphs.RandomGNP(6, .4).edges(labels=False)
[(0, 1), (0, 5), (1, 2), (2, 4), (3, 4), (3, 5), (4, 5)]
We plot a random graph on 12 nodes with probability `p = .71`::
sage: gnp = graphs.RandomGNP(12,.71)
sage: gnp.show() # long time
We view many random graphs using a graphics array::
sage: g = []
sage: j = []
sage: for i in range(9):
....: k = graphs.RandomGNP(i+3,.43)
....: g.append(k)
sage: for i in range(3):
....: n = []
....: for m in range(3):
....: n.append(g[3*i + m].plot(vertex_size=50, vertex_labels=False))
....: j.append(n)
sage: G = sage.plot.graphics.GraphicsArray(j)
sage: G.show() # long time
sage: graphs.RandomGNP(4,1)
Complete graph: Graph on 4 vertices
TESTS::
sage: graphs.RandomGNP(50,.2,method=50)
Traceback (most recent call last):
...
ValueError: 'method' must be equal to 'networkx' or to 'Sage'.
sage: set_random_seed(0)
sage: graphs.RandomGNP(50,.2, method="Sage").size()
243
sage: graphs.RandomGNP(50,.2, method="networkx").size()
258
"""
if n < 0:
raise ValueError("The number of nodes must be positive or null.")
if 0.0 > p or 1.0 < p:
raise ValueError("The probability p must be in [0..1].")
if seed is None:
seed = current_randstate().long_seed()
if p == 1:
from sage.graphs.generators.basic import CompleteGraph
return CompleteGraph(n)
if method == 'networkx':
import networkx
if fast:
G = networkx.fast_gnp_random_graph(n, p, seed=seed)
else:
G = networkx.gnp_random_graph(n, p, seed=seed)
return Graph(G)
elif method in ['Sage', 'sage']:
# We use the Sage generator
from sage.graphs.graph_generators_pyx import RandomGNP as sageGNP
return sageGNP(n, p)
else:
raise ValueError("'method' must be equal to 'networkx' or to 'Sage'.")
