Analysis module

Content

nngt.analysis.adjacency_matrix(graph, types=True, weights=True)[source]

Adjacency matrix of the graph.

Parameters:
  • graph (Graph or subclass) – Network to analyze.
  • types (bool, optional (default: True)) – Whether the excitatory/inhibitory type of the connnections should be considered (only if the weighing factor is the synaptic strength).
  • weights (bool or string, optional (default: True)) – Whether weights should be taken into account; if True, then connections are weighed by their synaptic strength, if False, then a binary matrix is returned, if weights is a string, then the ponderation is the correponding value of the edge attribute (e.g. “distance” will return an adjacency matrix where each connection is multiplied by its length).
Returns:

a csr_matrix.
nngt.analysis.assortativity(graph, deg_type='total')[source]

Assortativity of the graph.

Parameters:
  • graph (Graph or subclass) – Network to analyze.
  • deg_type (string, optional (default: ‘total’)) – Type of degree to take into account (among ‘in’, ‘out’ or ‘total’).
Returns:

a float quantifying the graph assortativity.
nngt.analysis.betweenness_distrib(graph, use_weights=True, nodes=None, num_nbins=None, num_ebins=None, log=False)[source]

Betweenness distribution of a graph.

Parameters:
  • graph (Graph or subclass) – the graph to analyze.
  • use_weights (bool, optional (default: True)) – use weighted degrees (do not take the sign into account : all weights are positive).
  • nodes (list or numpy.array of ints, optional (default: all nodes)) – Restrict the distribution to a set of nodes (only impacts the node attribute).
  • log (bool, optional (default: False)) – use log-spaced bins.
Returns:

  • ncounts (numpy.array) – number of nodes in each bin
  • nbetw (numpy.array) – bins for node betweenness
  • ecounts (numpy.array) – number of edges in each bin
  • ebetw (numpy.array) – bins for edge betweenness
nngt.analysis.closeness(graph, nodes=None, use_weights=False)[source]

Return the closeness centrality for each node in nodes.

Parameters:
  • graph (Graph object) – Graph to analyze.
  • nodes (array-like container with node ids, optional (default = all nodes)) – Nodes for which the local clustering coefficient should be computed.
  • use_weights (bool, optional (default: False)) – Whether weighted closeness should be used.
nngt.analysis.clustering(graph)[source]

Global clustering coefficient of the graph, defined as

\[c = 3 \times \frac{\text{triangles}}{\text{connected triples}}\]
nngt.analysis.degree_distrib(graph, deg_type='total', node_list=None, use_weights=False, log=False, num_bins=30)[source]

Degree distribution of a graph.

Parameters:
  • graph (Graph or subclass) – the graph to analyze.
  • deg_type (string, optional (default: “total”)) – type of degree to consider (“in”, “out”, or “total”).
  • node_list (list or numpy.array of ints, optional (default: None)) – Restrict the distribution to a set of nodes (default: all nodes).
  • use_weights (bool, optional (default: False)) – use weighted degrees (do not take the sign into account: all weights are positive).
  • log (bool, optional (default: False)) – use log-spaced bins.
Returns:

  • counts (numpy.array) – number of nodes in each bin
  • deg (numpy.array) – bins
nngt.analysis.diameter(graph)[source]

Pseudo-diameter of the graph @todo: weighted diameter

nngt.analysis.local_clustering(graph, nodes=None)[source]

Local clustering coefficient of the nodes, defined as

\[c_i = 3 \times \frac{\text{triangles}}{\text{connected triples}}\]
Parameters:
  • graph (Graph object) – Graph to analyze.
  • nodes (array-like container with node ids, optional (default = all nodes)) – Nodes for which the local clustering coefficient should be computed.
nngt.analysis.node_attributes(network, attributes, nodes=None)[source]

Return node attributes for a set of nodes.

Parameters:
  • network (Graph) – The graph where the nodes belong.
  • attributes (str or list) – Attributes which should be returned, among: * “betweenness” * “clustering” * “in-degree”, “out-degree”, “total-degree” * “subgraph_centrality”
  • nodes (list, optional (default: all nodes)) – Nodes for which the attributes should be returned.
Returns:

values (array-like or dict) – Returns the attributes, either as an array if only one attribute is required (attributes is a str) or as a dict of arrays.
nngt.analysis.num_iedges(graph)[source]

Returns the number of inhibitory connections.

nngt.analysis.num_scc(graph, listing=False)[source]

Returns the number of strongly connected components, i.e. ensembles where all nodes inside the ensemble can reach any other node in the ensemble using the directed edges.

See also

num_wcc()

nngt.analysis.num_wcc(graph, listing=False)[source]

Connected components if the directivity of the edges is ignored (i.e. all edges are considered as bidirectional).

See also

num_scc()

nngt.analysis.reciprocity(graph)[source]

Graph reciprocity, defined as \(E^\leftrightarrow/E\), where \(E^\leftrightarrow\) and \(E\) are, respectively, the number of bidirectional edges and the total number of edges in the graph.

Returns:a float quantifying the reciprocity.
nngt.analysis.spectral_radius(graph, typed=True, weighted=True)[source]

Spectral radius of the graph, defined as the eigenvalue of greatest module.

Parameters:
  • graph (Graph or subclass) – Network to analyze.
  • typed (bool, optional (default: True)) – Whether the excitatory/inhibitory type of the connnections should be considered.
  • weighted (bool, optional (default: True)) – Whether the weights should be taken into account.
Returns:

the spectral radius as a float.
nngt.analysis.subgraph_centrality(graph, weights=True, normalize='max_centrality')[source]

Subgraph centrality, accordign to [Estrada2005], for each node in the graph.

[Estrada2005]: Ernesto Estrada and Juan A. Rodríguez-Velázquez, Subgraph centrality in complex networks, PHYSICAL REVIEW E 71, 056103 (2005), available on ArXiv.

Parameters:
  • graph (Graph or subclass) – Network to analyze.
  • weights (bool or string, optional (default: True)) – Whether weights should be taken into account; if True, then connections are weighed by their synaptic strength, if False, then a binary matrix is returned, if weights is a string, then the ponderation is the correponding value of the edge attribute (e.g. “distance” will return an adjacency matrix where each connection is multiplied by its length).
  • normalize (str, optional (default: “max_centrality”)) – Whether the centrality should be normalized. Accepted normalizations are “max_eigenvalue” and “max_centrality”; the first rescales the adjacency matrix by the its largest eigenvalue before taking the exponential, the second sets the maximum centrality to one.
Returns:

centralities (numpy.ndarray) – The subgraph centrality of each node.