medusa.graph_theory package

Submodules

medusa.graph_theory.assortativity module

medusa.graph_theory.betweeenness_centrality module

medusa.graph_theory.betweeenness_centrality.betweenness(W, norm=True)[source]

Calculates the betweenness centrality of the graph, which is the probability that node i belong to one of the network shortest paths

Note: W must be converted to a connection-length matrix. It is common to obtain it via mapping from weight to length. BC is normalised to the range [0 1] as BC/[(N-1)(N-2)]

Parameters
  • W (numpy 2D matrix) – Graph matrix. ChannelsXChannels.

  • norm (bool) – Normalisation. 0 = no, 1 = yes. Default = True

Returns

BC – Network betweenness centrality.

Return type

numpy array

medusa.graph_theory.clustering_coefficient module

medusa.graph_theory.clustering_coefficient.clustering_coefficient(W, mode)[source]

Calculates the clustering coefficient.

Parameters
  • W (numpy 2D matrix) – Graph matrix. ChannelsXChannels.

  • mode (string) – GPU or CPU

Returns

nodal_clc – Nodal clustering coefficient

Return type

numpy array

medusa.graph_theory.complexity module

medusa.graph_theory.complexity.complexity(W, mode)[source]

Calculates the graph complexity.

Parameters
  • W (numpy 2D matrix) – Graph matrix. ChannelsXChannels.

  • mode (string) – GPU or CPU

Returns

global_comp – Global complexity.

Return type

numpy array

medusa.graph_theory.degree module

medusa.graph_theory.degree.degree(W, mode)[source]

Calculates the graph degree.

Parameters

W (numpy 2D matrix) – Graph matrix. ChannelsXChannels.

Returns

nodal_degree – Nodal degree.

Return type

numpy array

medusa.graph_theory.density module

medusa.graph_theory.density.density(W, mode)[source]

Calculates the graph density.

Parameters
  • W (numpy 2D matrix) – Graph matrix. ChannelsXChannels.

  • mode (string) – GPU or CPU

Returns

  • global_den (int) – Global density.

  • nodal_den (numpy array) – Nodal density.

medusa.graph_theory.efficiency module

medusa.graph_theory.efficiency.efficiency(W)[source]

Calculates the graph efficiency. Globally is the mean of the inverse shortests path length, and is inversely related to path length. Nodally/Locally is the same as globally but calculated on the neighbourhood of the node, and is related with clustering coefficient.

Parameters

W (numpy 2D matrix) – Graph matrix. ChannelsXChannels.

Returns

  • global_eff (numpy array) – Global efficiency.

  • nodal_eff (numpy array) – Nodal/Local efficiency.

medusa.graph_theory.eigen_centrality module

medusa.graph_theory.eigen_centrality.eigen_centrality(W)[source]

Calculates the eigenvector centrality, which is a centrality measure based on the adjacency matrix eigenvectors

Parameters
  • W (numpy 2D matrix) – Graph matrix. ChannelsXChannels.

  • mode (string) – GPU or CPU

Returns

nodal_eig – Nodal eigenvector centrality

Return type

numpy array

medusa.graph_theory.modularity module

medusa.graph_theory.modularity.modularity(W, gamma)[source]

Calculates the optimal node comunity and the modularity

Note: The optimal community structure subdivides the network in groups of nodes (non-overlapping), maximizing withing-groups edges while minimising between-groups edges. Modularity quantifies the degree to which the graph could be subdivided into the aforementioned communities

Parameters
  • W (numpy 2D matrix) – Graph matrix. ChannelsXChannels.

  • gamma (float) –

    modularity resolution parameter

    gamma>1 smaller modules 0<=gamma<1 larger modules gamma=1 (default) classic modularity function

Returns

  • Q (int) – Network modularity.

  • Ci (numpy array) – Network communities.

medusa.graph_theory.participation_coefficient module

medusa.graph_theory.participation_coefficient.participation_coefficient(W)[source]

Calculates the participation coefficient, which is the diversity of the between-module connections of each node

Parameters

W (numpy 2D matrix) – Graph matrix. ChannelsXChannels.

Returns

nodal_part – Nodal participation coefficient.

Return type

numpy array

medusa.graph_theory.path_length module

medusa.graph_theory.path_length.path_length(W, diagonal_dist=None, infinite_dist=None)[source]

Calculates the path length and other graph integration parameters

Note: L must be a connection-length matrix. One way of generating it is the inverse of the weight matrix.

Parameters

W (numpy 2D matrix) – Graph matrix. ChannelsXChannels.

Returns

  • global_pl (int) – Path lenght.

  • efficiency (int) – Network efficiency.

  • nodal_ecc (numpy array) – Network eccentricity.

  • radius (int) – Network radius.

  • diameter (int) – Network diameter.

  • nodal_d (numpy 2D matrix) – Shortest distances matrix.

medusa.graph_theory.surrogate_graph module

medusa.graph_theory.surrogate_graph.surrogate_graph(W)[source]

Calculates the graph degree.

Parameters

W (numpy 2D matrix) – Graph matrix. ChannelsXChannels.

Returns

surrog_W – Surrogated graph.

Return type

numpy array

medusa.graph_theory.transitivity module

medusa.graph_theory.transitivity.transitivity(W, mode)[source]

Calculates the transitivity, which is the number of triangles divided by the number of triples.

Parameters
  • W (numpy 2D matrix) – Graph matrix. ChannelsXChannels.

  • mode (string) – GPU or CPU

Returns

global_trans – Global transitivity.

Return type

int