def price_scale_free(m, c=None, gamma=1, nodes=0, weighted=True, directed=True,
seed_graph=None, multigraph=False, name="PriceSF",
shape=None, positions=None, population=None,
from_graph=None, **kwargs):
"""
@todo
make the algorithm.
Generate a Price graph model (Barabasi-Albert if undirected).
Parameters
----------
m : int
The number of edges each new node will make.
c : double
Constant added to the probability of a vertex receiving an edge.
gamma : double
Preferential attachment power.
nodes : int, optional (default: None)
The number of nodes in the graph.
weighted : bool, optional (default: True)
@todo
Whether the graph edges have weights.
directed : bool, optional (default: True)
Whether the graph is directed or not.
multigraph : bool, optional (default: False)
Whether the graph can contain multiple edges between two
nodes.
name : string, optional (default: "ER")
Name of the created graph.
shape : :class:`~nngt.geometry.Shape`, optional (default: None)
Shape of the neurons' environment
positions : :class:`numpy.ndarray`, optional (default: None)
A 2D or 3D array containing the positions of the neurons in space.
population : :class:`~nngt.NeuralPop`, optional (default: None)
Population of neurons defining their biological properties (to create a
:class:`~nngt.Network`).
from_graph : :class:`~nngt.Graph` or subclass, optional (default: None)
Initial graph whose nodes are to be connected.
Returns
-------
graph_price : :class:`~nngt.Graph` or subclass.
Note
----
`nodes` is required unless `from_graph` or `population` is provided.
"""
nodes = ( ( population.size if population is not None else nodes )
if from_graph is None else from_graph.node_nb() )
#~ c = c if c is not None else 0 if directed else 1
g = price_network(nodes, m, c, gamma, directed, seed_graph)
graph_obj_price = nngt.Graph.from_library(g)
graph_price = nngt.Graph.from_library(g)
_set_options(graph_price, population, shape, positions)
graph_price._graph_type = "price_scale_free"
return graph_price
def all_to_all(nodes=0,
weighted=True,
directed=True,
multigraph=False,
name="AlltoAll",
shape=None,
positions=None,
population=None,
**kwargs):
"""
Generate a graph where all nodes are connected.
.. versionadded:: 1.0
Parameters
----------
nodes : int, optional (default: None)
The number of nodes in the graph.
reciprocity : double, optional (default: -1 to let it free)
Fraction of edges that are bidirectional (only for directed graphs
-- undirected graphs have a reciprocity of 1 by definition)
weighted : bool, optional (default: True)
Whether the graph edges have weights.
directed : bool, optional (default: True)
Whether the graph is directed or not.
multigraph : bool, optional (default: False)
Whether the graph can contain multiple edges between two
nodes.
name : string, optional (default: "ER")
Name of the created graph.
shape : :class:`~nngt.geometry.Shape`, optional (default: None)
Shape of the neurons' environment.
positions : :class:`numpy.ndarray`, optional (default: None)
A 2D or 3D array containing the positions of the neurons in space.
population : :class:`~nngt.NeuralPop`, optional (default: None)
Population of neurons defining their biological properties (to create a
:class:`~nngt.Network`).
Note
----
`nodes` is required unless `population` is provided.
Returns
-------
graph_all : :class:`~nngt.Graph`, or subclass
A new generated graph.
"""
nodes = nodes if population is None else population.size
matrix = np.ones((nodes, nodes))
graph_all = nngt.Graph(name=name, nodes=nodes, directed=directed, **kwargs)
_set_options(graph_all, population, shape, positions)
# add edges
if nodes > 1:
ids = np.arange(nodes, dtype=np.uint)
edges = _all_to_all(ids, ids, directed, multigraph)
graph_all.new_edges(ia_edges)
graph_all._graph_type = "all_to_all"
return graph_all
def distance_rule(scale,
rule="exp",
shape=None,
neuron_density=1000.,
max_proba=-1.,
nodes=0,
density=-1.,
edges=-1,
avg_deg=-1.,
unit='um',
weighted=True,
directed=True,
multigraph=False,
name="DR",
positions=None,
population=None,
from_graph=None,
**kwargs):
"""
Create a graph using a 2D distance rule to create the connection between
neurons. Available rules are linear and exponential.
Parameters
----------
scale : float
Characteristic scale for the distance rule. E.g for linear distance-
rule, :math:`P(i,j) \propto (1-d_{ij}/scale))`, whereas for the
exponential distance-rule, :math:`P(i,j) \propto e^{-d_{ij}/scale}`.
rule : string, optional (default: 'exp')
Rule that will be apply to draw the connections between neurons.
Choose among "exp" (exponential), "gaussian" (Gaussian), or
"lin" (linear).
shape : :class:`~nngt.geometry.Shape`, optional (default: None)
Shape of the neurons' environment. If not specified, a square will be
created with the appropriate dimensions for the number of neurons and
the neuron spatial density.
neuron_density : float, optional (default: 1000.)
Density of neurons in space (:math:`neurons \cdot mm^{-2}`).
nodes : int, optional (default: None)
The number of nodes in the graph.
p : float, optional
Normalization factor for the distance rule; it is equal to the
probability of connection when testing a node at zero distance.
density: double, optional
Structural density given by `edges` / (`nodes` * `nodes`).
edges : int, optional
The number of edges between the nodes
avg_deg : double, optional
Average degree of the neurons given by `edges` / `nodes`.
unit : string (default: 'um')
Unit for the length `scale` among 'um' (:math:`\mu m`), 'mm', 'cm',
'dm', 'm'.
weighted : bool, optional (default: True)
@todo
Whether the graph edges have weights.
directed : bool, optional (default: True)
Whether the graph is directed or not.
multigraph : bool, optional (default: False)
Whether the graph can contain multiple edges between two
nodes.
name : string, optional (default: "DR")
Name of the created graph.
positions : :class:`numpy.ndarray`, optional (default: None)
A 2D (N, 2) or 3D (N, 3) shaped array containing the positions of the
neurons in space.
population : :class:`~nngt.NeuralPop`, optional (default: None)
Population of neurons defining their biological properties (to create a
:class:`~nngt.Network`).
from_graph : :class:`Graph` or subclass, optional (default: None)
Initial graph whose nodes are to be connected.
"""
distance = []
# convert neuronal density in (mu m)^2
neuron_density *= conversion_magnitude(unit, 'mm')**2
# set node number and library graph
graph_dr = from_graph
if graph_dr is not None:
nodes = graph_dr.node_nb()
graph_dr.clear_all_edges()
else:
nodes = population.size if population is not None else nodes
# check shape
if shape is None:
h = w = np.sqrt(float(nodes) / neuron_density)
shape = nngt.geometry.Shape.rectangle(h, w)
if graph_dr is None:
graph_dr = nngt.SpatialGraph(name=name,
nodes=nodes,
directed=directed,
shape=shape,
positions=positions,
**kwargs)
else:
Graph.make_spatial(graph_dr, shape, positions=positions)
positions = np.array(graph_dr.get_positions().T, dtype=np.float32)
# set options (graph has already been made spatial)
_set_options(graph_dr, population, None, None)
# add edges
ia_edges = None
conversion_factor = conversion_magnitude(shape.unit, unit)
if unit != shape.unit:
positions = np.multiply(conversion_factor, positions, dtype=np.float32)
if nodes > 1:
ids = np.arange(0, nodes, dtype=np.uint)
ia_edges = _distance_rule(ids,
ids,
density,
edges,
avg_deg,
scale,
rule,
max_proba,
shape,
positions,
directed,
multigraph,
distance=distance,
**kwargs)
attr = {'distance': distance}
# check for None if MPI
if ia_edges is not None:
graph_dr.new_edges(ia_edges, attributes=attr)
graph_dr._graph_type = "{}_distance_rule".format(rule)
return graph_dr
def newman_watts(coord_nb,
proba_shortcut,
nodes=0,
weighted=True,
directed=True,
multigraph=False,
name="NW",
shape=None,
positions=None,
population=None,
from_graph=None,
**kwargs):
"""
Generate a small-world graph using the Newman-Watts algorithm.
@todo
generate the edges of a circular graph to not replace the graph of the
`from_graph` and implement chosen reciprocity.
Parameters
----------
coord_nb : int
The number of neighbours for each node on the initial topological
lattice.
proba_shortcut : double
Probability of adding a new random (shortcut) edge for each existing
edge on the initial lattice.
nodes : int, optional (default: None)
The number of nodes in the graph.
density: double, optional (default: 0.1)
Structural density given by `edges` / (`nodes`*`nodes`).
edges : int (optional)
The number of edges between the nodes
avg_deg : double, optional
Average degree of the neurons given by `edges` / `nodes`.
weighted : bool, optional (default: True)
@todo
Whether the graph edges have weights.
directed : bool, optional (default: True)
Whether the graph is directed or not.
multigraph : bool, optional (default: False)
Whether the graph can contain multiple edges between two
nodes.
name : string, optional (default: "ER")
Name of the created graph.
shape : :class:`~nngt.geometry.Shape`, optional (default: None)
Shape of the neurons' environment
positions : :class:`numpy.ndarray`, optional (default: None)
A 2D or 3D array containing the positions of the neurons in space.
population : :class:`~nngt.NeuralPop`, optional (default: None)
Population of neurons defining their biological properties (to create a
:class:`~nngt.Network`).
from_graph : :class:`Graph` or subclass, optional (default: None)
Initial graph whose nodes are to be connected.
Returns
-------
graph_nw : :class:`~nngt.Graph` or subclass
Note
----
`nodes` is required unless `from_graph` or `population` is provided.
"""
# set node number and library graph
graph_nw = from_graph
if graph_nw is not None:
nodes = graph_nw.node_nb()
graph_nw.clear_all_edges()
else:
nodes = population.size if population is not None else nodes
graph_nw = nngt.Graph(name=name,
nodes=nodes,
directed=directed,
**kwargs)
_set_options(graph_nw, population, shape, positions)
# add edges
ia_edges = None
if nodes > 1:
ids = range(nodes)
ia_edges = _newman_watts(ids, ids, coord_nb, proba_shortcut, directed,
multigraph)
graph_nw.new_edges(ia_edges)
graph_nw._graph_type = "newman_watts"
return graph_nw
def random_scale_free(in_exp,
out_exp,
nodes=0,
density=-1,
edges=-1,
avg_deg=-1,
reciprocity=0.,
weighted=True,
directed=True,
multigraph=False,
name="RandomSF",
shape=None,
positions=None,
population=None,
from_graph=None,
**kwargs):
"""
Generate a free-scale graph of given reciprocity and otherwise
devoid of correlations.
Parameters
----------
in_exp : float
Absolute value of the in-degree exponent :math:`\gamma_i`, such that
:math:`p(k_i) \propto k_i^{-\gamma_i}`
out_exp : float
Absolute value of the out-degree exponent :math:`\gamma_o`, such that
:math:`p(k_o) \propto k_o^{-\gamma_o}`
nodes : int, optional (default: None)
The number of nodes in the graph.
density: double, optional (default: 0.1)
Structural density given by `edges / (nodes*nodes)`.
edges : int (optional)
The number of edges between the nodes
avg_deg : double, optional
Average degree of the neurons given by `edges / nodes`.
weighted : bool, optional (default: True)
@todo
Whether the graph edges have weights.
directed : bool, optional (default: True)
Whether the graph is directed or not.
multigraph : bool, optional (default: False)
Whether the graph can contain multiple edges between two
nodes. can contain multiple edges between two
name : string, optional (default: "ER")
Name of the created graph.
shape : :class:`~nngt.geometry.Shape`, optional (default: None)
Shape of the neurons' environment.
positions : :class:`numpy.ndarray`, optional (default: None)
A 2D or 3D array containing the positions of the neurons in space.
population : :class:`~nngt.NeuralPop`, optional (default: None)
Population of neurons defining their biological properties (to create a
:class:`~nngt.Network`)
from_graph : :class:`Graph` or subclass, optional (default: None)
Initial graph whose nodes are to be connected.
Returns
-------
graph_fs : :class:`~nngt.Graph`
Note
----
As reciprocity increases, requested values of `in_exp` and `out_exp`
will be less and less respected as the distribution will converge to a
common exponent :math:`\gamma = (\gamma_i + \gamma_o) / 2`.
Parameter `nodes` is required unless `from_graph` or `population` is
provided.
"""
# set node number and library graph
graph_rsf = from_graph
if graph_rsf is not None:
nodes = graph_rsf.node_nb()
graph_rsf.clear_all_edges()
else:
nodes = population.size if population is not None else nodes
graph_rsf = nngt.Graph(name=name,
nodes=nodes,
directed=directed,
**kwargs)
_set_options(graph_rsf, population, shape, positions)
# add edges
ia_edges = None
if nodes > 1:
ids = range(nodes)
ia_edges = _random_scale_free(ids, ids, in_exp, out_exp, density,
edges, avg_deg, reciprocity, directed,
multigraph)
graph_rsf.new_edges(ia_edges)
graph_rsf._graph_type = "random_scale_free"
return graph_rsf
def erdos_renyi(density=-1.,
nodes=0,
edges=-1,
avg_deg=-1.,
reciprocity=-1.,
weighted=True,
directed=True,
multigraph=False,
name="ER",
shape=None,
positions=None,
population=None,
from_graph=None,
**kwargs):
"""
Generate a random graph as defined by Erdos and Renyi but with a
reciprocity that can be chosen.
Parameters
----------
density : double, optional (default: -1.)
Structural density given by `edges / nodes`:math:`^2`. It is also the
probability for each possible edge in the graph to exist.
nodes : int, optional (default: None)
The number of nodes in the graph.
edges : int (optional)
The number of edges between the nodes
avg_deg : double, optional
Average degree of the neurons given by `edges / nodes`.
reciprocity : double, optional (default: -1 to let it free)
Fraction of edges that are bidirectional (only for
directed graphs -- undirected graphs have a reciprocity of 1 by
definition)
weighted : bool, optional (default: True)
Whether the graph edges have weights.
directed : bool, optional (default: True)
Whether the graph is directed or not.
multigraph : bool, optional (default: False)
Whether the graph can contain multiple edges between two
nodes.
name : string, optional (default: "ER")
Name of the created graph.
shape : :class:`~nngt.geometry.Shape`, optional (default: None)
Shape of the neurons' environment.
positions : :class:`numpy.ndarray`, optional (default: None)
A 2D or 3D array containing the positions of the neurons in space.
population : :class:`~nngt.NeuralPop`, optional (default: None)
Population of neurons defining their biological properties (to create a
:class:`~nngt.Network`).
from_graph : :class:`Graph` or subclass, optional (default: None)
Initial graph whose nodes are to be connected.
Returns
-------
graph_er : :class:`~nngt.Graph`, or subclass
A new generated graph or the modified `from_graph`.
Note
----
`nodes` is required unless `from_graph` or `population` is provided.
If an `from_graph` is provided, all preexistant edges in the
object will be deleted before the new connectivity is implemented.
"""
# set node number and library graph
graph_er = from_graph
if graph_er is not None:
nodes = graph_er.node_nb()
graph_er.clear_all_edges()
else:
nodes = population.size if population is not None else nodes
graph_er = nngt.Graph(name=name,
nodes=nodes,
directed=directed,
**kwargs)
_set_options(graph_er, population, shape, positions)
# add edges
ia_edges = None
if nodes > 1:
ids = range(nodes)
ia_edges = _erdos_renyi(ids, ids, density, edges, avg_deg, reciprocity,
directed, multigraph)
graph_er.new_edges(ia_edges)
graph_er._graph_type = "erdos_renyi"
return graph_er
def gaussian_degree(avg,
std,
degree_type='in',
nodes=0,
reciprocity=-1.,
weighted=True,
directed=True,
multigraph=False,
name="GD",
shape=None,
positions=None,
population=None,
from_graph=None,
**kwargs):
"""
Generate a random graph with constant in- or out-degree.
@todo: adapt it for undirected graphs!
Parameters
----------
avg : float
The value of the average degree.
std : float
The standard deviation of the Gaussian distribution.
degree_type : str, optional (default: 'in')
The type of the fixed degree, among 'in', 'out' or 'total'
@todo: Implement 'total' degree
nodes : int, optional (default: None)
The number of nodes in the graph.
reciprocity : double, optional (default: -1 to let it free)
@todo: not implemented yet. Fraction of edges that are bidirectional
(only for directed graphs -- undirected graphs have a reciprocity of
1 by definition)
weighted : bool, optional (default: True)
Whether the graph edges have weights.
directed : bool, optional (default: True)
@todo: only for directed graphs for now. Whether the graph is directed
or not.
multigraph : bool, optional (default: False)
Whether the graph can contain multiple edges between two
nodes.
name : string, optional (default: "ER")
Name of the created graph.
shape : :class:`~nngt.geometry.Shape`, optional (default: None)
Shape of the neurons' environment.
positions : :class:`numpy.ndarray`, optional (default: None)
A 2D or 3D array containing the positions of the neurons in space.
population : :class:`~nngt.NeuralPop`, optional (default: None)
Population of neurons defining their biological properties (to create a
:class:`~nngt.Network`).
from_graph : :class:`Graph` or subclass, optional (default: None)
Initial graph whose nodes are to be connected.
Returns
-------
graph_gd : :class:`~nngt.Graph`, or subclass
A new generated graph or the modified `from_graph`.
Note
----
`nodes` is required unless `from_graph` or `population` is provided.
If an `from_graph` is provided, all preexistant edges in the object
will be deleted before the new connectivity is implemented.
"""
# set node number and library graph
graph_gd = from_graph
if graph_gd is not None:
nodes = graph_gd.node_nb()
graph_gd.clear_all_edges()
else:
nodes = population.size if population is not None else nodes
graph_gd = nngt.Graph(name=name,
nodes=nodes,
directed=directed,
**kwargs)
_set_options(graph_gd, population, shape, positions)
# add edges
ia_edges = None
if nodes > 1:
ids = np.arange(nodes, dtype=np.uint)
ia_edges = _gaussian_degree(ids, ids, avg, std, degree_type,
reciprocity, directed, multigraph)
# check for None if MPI
if ia_edges is not None:
graph_gd.new_edges(ia_edges)
graph_gd._graph_type = "gaussian_{}_degree".format(degree_type)
return graph_gd