def duplication_divergence_iky(n, s, **kwargs):
"""
Generate a random graph using the duplication-divergence model proposed by Ispolatov, Krapivski, and Yuryev (2008).
**Args**:
* ``n`` (int): the target size of the network.
* ``s`` (float): the probability that a link connected to a newly duplicated node will exist
**KwArgs**:
* ``directed [=False]`` (boolean): whether to build the graph directed. If ``True``, then the ``m`` edges created
by a node upon its creation are instantiated as out-edges. All others are in-edges to that node.
* ``seed [=-1]`` (int): a seed for the random number generator
* ``graph [=None]`` (:py:class:`zen.Graph` or :py:class:`zen.DiGraph`): this is the actual graph instance to populate. It must be
empty and its directionality must agree with the value of ``directed``.
**Returns**:
:py:class:`zen.Graph` or :py:class:`zen.DiGraph`. The graph generated. If ``directed = True``, then a :py:class:`DiGraph` will be returned.
.. note::
Source: I. Ispolatov, P. L. Krapivski, and A. Yuryev "Duplication-divergence model of protein interaction network", ??, 2008.
"""
seed = kwargs.pop('seed',None)
directed = kwargs.pop('directed',False)
graph = kwargs.pop('graph',None)
if graph is not None:
if len(graph) > 0:
raise ZenException, 'the graph must be empty, if provided'
if graph.is_directed() != directed:
raise ZenException, 'graph and directed arguments must agree'
if len(kwargs) > 0:
raise ZenException, 'Unknown arguments: %s' % ', '.join(kwargs.keys())
if seed is None:
seed = -1
# initialize the random number generator
if seed >= 0:
random.seed(seed)
if type(n) != int:
raise ZenException, 'Parameter n must be an integer'
if type(s) != float and type(s) != int and type(s) != double:
print type(s)
raise ZenException, 'Parameter s must be a float, double, or an int'
G = graph
if graph is None:
if directed:
G = DiGraph()
else:
G = Graph()
# initialize the graph with two connected nodes
G.add_edge(0,1)
# build the rest of the graph
i = 2
while i < n:
# pick an existing node to copy
cn_seed = random.randint(0,100000)
u = choose_node(G,seed=cn_seed)
#####
# create the partial copy
G.add_node(i)
# copy edges
if not directed:
for w in G.neighbors(u):
if random.random() <= s:
G.add_edge(i,w)
else:
for w in G.in_neighbors(u):
if random.random() <= s:
G.add_edge(w,i)
for w in G.out_neighbors(u):
if random.random() <= s:
G.add_edge(i,w)
# if the node doesn't have any connections, then ditch it
if G.degree(i) == 0:
G.rm_node(i)
else:
i += 1
# done!
return G
def local_attachment(n, m, r, **kwargs):
"""
Generate a random graph using the local attachment model.
**Args**:
* ``n`` (int): the number of nodes to add to the graph
* ``m`` (int): the number of edges a new node will add to the graph
* ``r`` (int): the number of edges (of the ``m``) that a node will add to uniformly selected random nodes.
All others will be added to neighbors of the ``r`` selected nodes.
**KwArgs**:
* ``seed [=-1]`` (int): a seed for the random number generator
* ``graph [=None]`` (:py:class:`zen.DiGraph`): the graph that will be populated. If the graph is ``None``,
then a new graph will be created.
**Returns**:
:py:class:`zen.DiGraph`. The graph generated.
.. note::
Source: M. O. Jackson and B. O. Rogers "Meeting strangers and friends of friends: How random are social networks?" The American Economic Review, 2007.
"""
seed = kwargs.pop('seed', None)
graph = kwargs.pop('graph', None)
if graph is not None and not graph.is_directed():
raise ZenException, 'The graph provided must be directed'
if graph is not None and len(graph) > 0:
raise ZenException, 'The graph provided is not empty'
if len(kwargs) > 0:
raise ZenException, 'Unknown arguments: %s' % ', '.join(kwargs.keys())
if type(r) != int:
raise ZenException, 'r must be an integer'
elif r < 1:
raise ZenException, 'r must be 1 or larger'
if seed is None:
seed = -1
if seed >= 0:
random.seed(seed)
#####
# build the initial graph
G = graph
if G is None:
G = DiGraph()
# populate with nodes
for i in range(m + 1):
G.add_node(i)
# according to Jackson's paper, all initial nodes have m neighbors.
for i in range(m + 1):
for j in range(m + 1):
if j != i:
G.add_edge(j, i)
######
# Build the rest of the graph
node_list = list(range(m + 1))
for i in range(m + 1, n):
G.add_node(i)
# pick random neighbors (the parents)
parents = random.sample(node_list, r)
# pick neighbors from the parents' neighborhoods
potentials = set()
for n in parents:
potentials.update(G.out_neighbors(n))
potentials.difference_update(parents)
nsize = min([m - r, len(potentials)])
neighbors = random.sample(potentials, nsize)
# connect
for v in (parents + neighbors):
G.add_edge(i, v)
node_list.append(i)
# done
return G
def duplication_divergence_iky(n, s, **kwargs):
"""
Generate a random graph using the duplication-divergence model proposed by Ispolatov, Krapivski, and Yuryev (2008).
**Args**:
* ``n`` (int): the target size of the network.
* ``s`` (float): the probability that a link connected to a newly duplicated node will exist
**KwArgs**:
* ``directed [=False]`` (boolean): whether to build the graph directed. If ``True``, then the ``m`` edges created
by a node upon its creation are instantiated as out-edges. All others are in-edges to that node.
* ``seed [=-1]`` (int): a seed for the random number generator
* ``graph [=None]`` (:py:class:`zen.Graph` or :py:class:`zen.DiGraph`): this is the actual graph instance to populate. It must be
empty and its directionality must agree with the value of ``directed``.
**Returns**:
:py:class:`zen.Graph` or :py:class:`zen.DiGraph`. The graph generated. If ``directed = True``, then a :py:class:`DiGraph` will be returned.
.. note::
Source: I. Ispolatov, P. L. Krapivski, and A. Yuryev "Duplication-divergence model of protein interaction network", ??, 2008.
"""
seed = kwargs.pop('seed', None)
directed = kwargs.pop('directed', False)
graph = kwargs.pop('graph', None)
if graph is not None:
if len(graph) > 0:
raise ZenException, 'the graph must be empty, if provided'
if graph.is_directed() != directed:
raise ZenException, 'graph and directed arguments must agree'
if len(kwargs) > 0:
raise ZenException, 'Unknown arguments: %s' % ', '.join(kwargs.keys())
if seed is None:
seed = -1
# initialize the random number generator
if seed >= 0:
random.seed(seed)
if type(n) != int:
raise ZenException, 'Parameter n must be an integer'
if type(s) != float and type(s) != int and type(s) != double:
print type(s)
raise ZenException, 'Parameter s must be a float, double, or an int'
G = graph
if graph is None:
if directed:
G = DiGraph()
else:
G = Graph()
# initialize the graph with two connected nodes
G.add_edge(0, 1)
# build the rest of the graph
i = 2
while i < n:
# pick an existing node to copy
cn_seed = random.randint(0, 100000)
u = choose_node(G, seed=cn_seed)
#####
# create the partial copy
G.add_node(i)
# copy edges
if not directed:
for w in G.neighbors(u):
if random.random() <= s:
G.add_edge(i, w)
else:
for w in G.in_neighbors(u):
if random.random() <= s:
G.add_edge(w, i)
for w in G.out_neighbors(u):
if random.random() <= s:
G.add_edge(i, w)
# if the node doesn't have any connections, then ditch it
if G.degree(i) == 0:
G.rm_node(i)
else:
i += 1
# done!
return G
def local_attachment(n, m, r, **kwargs):
"""
Generate a random graph using the local attachment model.
**Args**:
* ``n`` (int): the number of nodes to add to the graph
* ``m`` (int): the number of edges a new node will add to the graph
* ``r`` (int): the number of edges (of the ``m``) that a node will add to uniformly selected random nodes.
All others will be added to neighbors of the ``r`` selected nodes.
**KwArgs**:
* ``seed [=-1]`` (int): a seed for the random number generator
* ``graph [=None]`` (:py:class:`zen.DiGraph`): the graph that will be populated. If the graph is ``None``,
then a new graph will be created.
**Returns**:
:py:class:`zen.DiGraph`. The graph generated.
.. note::
Source: M. O. Jackson and B. O. Rogers "Meeting strangers and friends of friends: How random are social networks?" The American Economic Review, 2007.
"""
seed = kwargs.pop('seed',None)
graph = kwargs.pop('graph',None)
if graph is not None and not graph.is_directed():
raise ZenException, 'The graph provided must be directed'
if graph is not None and len(graph) > 0:
raise ZenException, 'The graph provided is not empty'
if len(kwargs) > 0:
raise ZenException, 'Unknown arguments: %s' % ', '.join(kwargs.keys())
if type(r) != int:
raise ZenException, 'r must be an integer'
elif r < 1:
raise ZenException, 'r must be 1 or larger'
if seed is None:
seed = -1
if seed >= 0:
random.seed(seed)
#####
# build the initial graph
G = graph
if G is None:
G = DiGraph()
# populate with nodes
for i in range(m+1):
G.add_node(i)
# according to Jackson's paper, all initial nodes have m neighbors.
for i in range(m+1):
for j in range(m+1):
if j != i:
G.add_edge(j,i)
######
# Build the rest of the graph
node_list = list(range(m+1))
for i in range(m+1,n):
G.add_node(i)
# pick random neighbors (the parents)
parents = random.sample(node_list,r)
# pick neighbors from the parents' neighborhoods
potentials = set()
for n in parents:
potentials.update(G.out_neighbors(n))
potentials.difference_update(parents)
nsize = min([m-r,len(potentials)])
neighbors = random.sample(potentials,nsize)
# connect
for v in (parents + neighbors):
G.add_edge(i,v)
node_list.append(i)
# done
return G
