Generation module

Functions that generates the underlying connectivity of graphs, as well as the synaptic properties (weight/strength and delay).

Content

nngt.generation.connect_neural_groups(network, source_groups, target_groups, graph_model, model_param)

Function to connect excitatory and inhibitory population with a given graph model. .. todo

make the modifications for only a set of edges

Parameters:

• network (Network or SpatialNetwork) – The network to connect.
• source_groups (tuple of strings) – Names of the source groups (which contain the pre-synaptic neurons)
• target_groups (tuple of strings) – Names of the target groups (which contain the post-synaptic neurons)
• graph_model (string) – The name of the connectivity model (among “erdos_renyi”, “random_scale_free”, “price_scale_free”, and “newman_watts”).
• model_param (dict) – Dictionary containing the model parameters (the keys are the keywords of the associated generation function — see above).

nngt.generation.connect_neural_types(network, source_type, target_type, graph_model, model_param, weighted=True)

Function to connect excitatory and inhibitory population with a given graph model. .. todo

make the modifications for only a set of edges

Parameters:

• network (Network or SpatialNetwork) – The network to connect.
• source_type (int) – The type of source neurons (1 for excitatory, ``-1 for inhibitory neurons).
• source_type (int) – The type of target neurons.
• graph_model (string) – The name of the connectivity model (among “erdos_renyi”, “random_scale_free”, “price_scale_free”, and “newman_watts”).
• model_param (dict) – Dictionary containing the model parameters (the keys are the keywords of the associated generation function — see above).
• weighted (bool, optional (default: True)) – @todo Whether the graph edges have weights.

nngt.generation.distance_rule(scale, rule='exp', shape=None, neuron_density=1000.0, nodes=0, density=0.1, edges=-1, avg_deg=-1.0, 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, \(P(i,j) \propto (1-d_{ij}/scale))\), whereas for the exponential distance-rule, \(P(i,j) \propto e^{-d_{ij}/scale}\).
• rule (string, optional (default: ‘exp’)) – Rule that will be apply to draw the connections between neurons. Choose among “exp” (exponential), “lin” (linear, not implemented yet), “power” (power-law, not implemented yet).
• shape (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 (\(neurons \cdot mm^{-2}\)).
• 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: “DR”)) – Name of the created graph.
• positions (numpy.ndarray, optional (default: None)) – A 2D or 3D array containing the positions of the neurons in space.
• population (NeuralPop, optional (default: None)) – Population of neurons defining their biological properties (to create a Network).
• from_graph (Graph or subclass, optional (default: None)) – Initial graph whose nodes are to be connected.

nngt.generation.erdos_renyi(nodes=0, density=0.1, edges=-1, avg_deg=-1.0, reciprocity=-1.0, 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:

• nodes (int, optional (default: None)) – The number of nodes in the graph.
• density (double, optional (default: 0.1)) – Structural density given by edges / nodes\(^2\).
• 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 (Shape, optional (default: None)) – Shape of the neurons’ environment.
• positions (numpy.ndarray, optional (default: None)) – A 2D or 3D array containing the positions of the neurons in space.
• population (NeuralPop, optional (default: None)) – Population of neurons defining their biological properties (to create a Network).
• from_graph (Graph or subclass, optional (default: None)) – Initial graph whose nodes are to be connected.

Returns:

graph_er (Graph, or subclass) – A new generated graph or the modified from_graph.

Notes

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.

nngt.generation.fixed_degree(degree, degree_type='in', nodes=0, reciprocity=-1.0, weighted=True, directed=True, multigraph=False, name='ER', shape=None, positions=None, population=None, from_graph=None, **kwargs)

Generate a random graph with constant in- or out-degree.

Parameters:

• degree (int) – The value of the constant degree.
• degree_type (str, optional (default: ‘in’)) – The type of the fixed degree, among ‘in’, ‘out’ or ‘total’ (@todo: not implemented yet).
• 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 (Shape, optional (default: None)) – Shape of the neurons’ environment.
• positions (numpy.ndarray, optional (default: None)) – A 2D or 3D array containing the positions of the neurons in space.
• population (NeuralPop, optional (default: None)) – Population of neurons defining their biological properties (to create a Network).
• from_graph (Graph or subclass, optional (default: None)) – Initial graph whose nodes are to be connected.

Returns:

graph_er (Graph, or subclass) – A new generated graph or the modified from_graph.

Notes

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.

nngt.generation.random_scale_free(in_exp, out_exp, nodes=0, density=0.1, edges=-1, avg_deg=-1, reciprocity=0.0, 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.

in_exp : float

Absolute value of the in-degree exponent \(\gamma_i\), such that :math:`p(k_i) propto k_i^{-gamma_i}

out_exp : float

Absolute value of the out-degree exponent \(\gamma_o\), 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 : Shape, optional (default: None)

Shape of the neurons’ environment.

positions : numpy.ndarray, optional (default: None)

A 2D or 3D array containing the positions of the neurons in space.

population : NeuralPop, optional (default: None)

Population of neurons defining their biological properties (to create a Network)

from_graph : Graph or subclass, optional (default: None)

Initial graph whose nodes are to be connected.

graph_fs : Graph

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 =

rac{gamma_i + gamma_o}{2}`.

Parameter nodes is required unless from_graph or population is provided.

nngt.generation.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)

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 (Shape, optional (default: None)) – Shape of the neurons’ environment
• positions (numpy.ndarray, optional (default: None)) – A 2D or 3D array containing the positions of the neurons in space.
• population (NeuralPop, optional (default: None)) – Population of neurons defining their biological properties (to create a Network).
• from_graph (Graph or subclass, optional (default: None)) – Initial graph whose nodes are to be connected.

Returns:

graph_price (Graph or subclass.)

Notes

nodes is required unless from_graph or population is provided.

nngt.generation.newman_watts(coord_nb, proba_shortcut, nodes=0, 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 (Shape, optional (default: None)) – Shape of the neurons’ environment
• positions (numpy.ndarray, optional (default: None)) – A 2D or 3D array containing the positions of the neurons in space.
• population (NeuralPop, optional (default: None)) – Population of neurons defining their biological properties (to create a Network).
• from_graph (Graph or subclass, optional (default: None)) – Initial graph whose nodes are to be connected.

Returns:

graph_nw (Graph or subclass)

Notes

nodes is required unless from_graph or population is provided.