Classes, Solvers and Utilities

Undirected Graph

class DyGyS.Undirected_class.UndirectedGraph(adjacency=None)

Undirected Graph instance must be initialised with adjacency weighted matrix On initialization it computes also the core network statistics and the binary adjacency matrix.

Parameters

adjacency (np.ndarray, list) – Weighted adjacency matrix

classification_measures(n_ensemble=1000, percentiles=(2.5, 97.5), stats=[])

Computes Measures for the quality of classification, listed in self.implemented_classifier_statistics. To be used after .solve() :param n_ensemble: Wanted number of ensemble graphs, default is 1000. :type n_ensemble: int

Parameters

• percentiles (tuple) – Explicit the percentiles used for the construction of the confidence interval, default is (2.5,97.5) for a 95 CI.

• stats (list of strings) – numpy array or list of classifier statistics in string format.

gen_ensemble(n_ensemble=1000)

Generate an ensemble of -n_ensemble- networks according to the selected model

Parameters

n_ensemble (int) – Number of wanted Graph realizations

Returns

N_obs X n_ensemble numpy matrix that collects all the ensemble adjacency matrices

Return type

np.ndarray

netstats_measures(percentiles=(2.5, 97.5), stats=[])

Computes available network statistics, To be used after .solve() and .gen_ensemble().

Parameters

• percentiles (Tuple) – Explicit the percentiles used for the construction of the confidence interval, default is (2.5,97.5) for a 95 CI.

• stats (list) – numpy array or list of available network statistics. The wanted stats must be in the list -.implemented_network_statistics-

reproduction_accuracy_s(percentiles=(2.5, 97.5), stats=[])

Computes RA_s, the percentage of nodes for which the network statistics are compatible with the graph ensemble according to a percentile confidence interval. To be used after .solve() and .gen_ensemble().

Parameters

• percentiles (tuple) – Explicit the percentiles used for the construction of the confidence interval, default is (2.5,97.5) for a 95 CI.

• stats (list of strings) – numpy array or list of network statistics for which it is possible to recover RA_s. The wanted stats must be in the list -.implemented_network_statistics-

Returns

L-list where L is the number of statistics, the order follows the input stats array

Return type

list of float

reproduction_accuracy_w(percentiles=(2.5, 97.5))

Computes RA_w, the percentage of couples for which the weights are compatible with the graph ensemble according to a percentile confidence interval. To be used after .solve() and .gen_ensemble().

Parameters

percentiles (Tuple) – Explicit the percentiles used for the construction of the confidence interval, default is (2.5,97.5) for a 95 CI.

Returns

A number (0,1) that explicits RA_w

Return type

np.ndarray

solver(model, exogenous_variables=numpy.array, selection_variables=numpy.array, fixed_selection_params=numpy.array, verbose=False, print_steps=numpy.inf, imported_params=numpy.array, use_guess=numpy.array, maxiter=10, tol=1e-05)

Optimize chosen model for Undirected Graphs and compute model selection measures such as AIC and BIC.

Parameters

• model (string) – Chosen model

• exogenous_variables (np.ndarray) – Exogenous Variables used for the weighted step, in numpy 2-D format of the type N X k where N are the observations and k are the params,

• selection_variables (np.ndarray) – Exogenous Variables used for the topological step, in numpy 2-D format of the type N X k where N are the observations and k are the params,

• fixed_selection_params (np.ndarray) – Optional Constant Parameters for the topological step. When initialized different from null vector, it fixes the last “n” topological parameters, when selection_variables are used and n is the size of fixed_selection_params

• verbose (boolean) – True if you want to see every n*print_steps iterations, default is False

• print_steps (int) – If verbose is True, you print on screen every n*print_steps iterations. default is 1

• imported_params (np.ndarray) – If used, uses wanted params as solution.

• use_guess (np.ndarray) – If used, uses wanted params as starters in the optimization.

• maxiter (int) – Maximum Iterations of solver function.

• tol (float) – tolerance for infinite norm in the optimization process

Directed Graph

class DyGyS.Directed_class.DirectedGraph(adjacency=None)

“Directed Graph instance must be initialised with adjacency weighted matrix. An exploratory analysis is conducted during initialization. See .implemented_models, .implemented_network_statistics and .implemented_classifier_statistics for available methods and statistics.

Params adjacency (np.ndarray,list)

Weighted adjacency matrix in numpy 1D, numpy 2D or list format.

classification_measures(n_ensemble=1000, percentiles=(2.5, 97.5), stats=[])

Computes Measures for the quality of classification, listed in self.implemented_classifier_statistics. To be used after .solve() :param n_ensemble: Wanted number of ensemble graphs, default is 1000. :type n_ensemble: int

Parameters

• percentiles (tuple) – Explicit the percentiles used for the construction of the confidence interval, default is (2.5,97.5) for a 95 CI.

• stats (list of strings) – numpy array or list of classifier statistics in string format.

Returns

Average value, standard deviation, percentiles and ensemble distribution of * classifier statistic in the graph ensemble.

Return type

float, float, tuple, np.ndarray

gen_ensemble(n_ensemble=1000)

Generate an ensemble of -n_ensemble- networks according to the selected model

Parameters

n_ensemble (int) – Number of wanted Graph realizations

Returns

N_obs X n_ensemble numpy matrix that collects all the ensemble adjacency matrices

Return type

np.ndarray

netstats_measures(percentiles=(2.5, 97.5), stats=[])

Computes available network statistics, To be used after .solve() and .gen_ensemble(). Available attributes are .avg_*, .std_*, .percentiles_* and .array_* where * stands for the wanted statistics, avg_* is namely the ensemble average, std_* is the ensemble standard deviation, percentiles_* is a Tuple made by (percentile[0],percentile[1]) of the ensemble distribution, array_* is the whole ensemble distribution.

Parameters

• percentiles (Tuple) – Explicit the percentiles used for the construction of the confidence interval, default is (2.5,97.5) for a 95 CI.

• stats (list) – numpy array or list of available network statistics. The wanted stats must be in the list -.implemented_network_statistics-

reproduction_accuracy_s(percentiles=(2.5, 97.5), stats=[])

Computes RA_s, the percentage of nodes for which the network statistics are compatible with the graph ensemble according to a percentile confidence interval. To be used after .solve() and .gen_ensemble().

Parameters

• percentiles (tuple) – Explicit the percentiles used for the construction of the confidence interval, default is (2.5,97.5) for a 95 CI.

• stats (list of strings) – numpy array or list of network statistics for which it is possible to recover RA_s. The wanted stats must be in the list -.implemented_network_statistics-

Returns

L-list where L is the number of statistics, the order follows the input stats array

Return type

list of float

reproduction_accuracy_w(percentiles=(2.5, 97.5))

Computes RA_w, the percentage of couples for which the weights are compatible with the graph ensemble according to a percentile confidence interval. To be used after .solve() and .gen_ensemble().

Parameters

percentiles (Tuple) – Explicit the percentiles used for the construction of the confidence interval, default is (2.5,97.5) for a 95 CI.

Returns

A number (0,1) that explicits RA_w

Return type

np.ndarray

solver(model, exogenous_variables=numpy.array, selection_variables=numpy.array, fixed_selection_params=numpy.array, verbose=False, print_steps=1, imported_params=numpy.array, use_guess=numpy.array, maxiter=10, tol=1e-05)

Optimize chosen model for Directed Graphs and compute model selection measures such as AIC and BIC.

Parameters

• model (string) – Chosen model

• exogenous_variables (np.ndarray) – Exogenous Variables used for the weighted step, in numpy 2-D format of the type N X k where N are the observations and k are the params,

• selection_variables (np.ndarray) – Exogenous Variables used for the topological step, in numpy 2-D format of the type N X k where N are the observations and k are the params,

• fixed_selection_params (np.ndarray) – Optional Constant Parameters for the topological step. When initialized different from null vector, it fixes the last “n” topological parameters, when selection_variables are used and n is the size of fixed_selection_params

• verbose (boolean) – True if you want to see every n*print_steps iterations, default is False

• print_steps (int) – If verbose is True, you print on screen every n*print_steps iterations. default is 1

• print_steps – number of steps for which you can investigate iterations, if Verbose is True

• imported_params (np.ndarray) – If used, uses wanted params as solution.

• use_guess (np.ndarray) – If used, uses wanted params as starters in the optimization.

• maxiter (int) – Maximum Iterations of solver function.

• tol (float) – tolerance for infinite norm in the optimization process

Ensemble Functions

DyGyS.ensemble_Functions.IT_sampling_Exponential(random_array, zij, beta_0, n_ensemble)

Inverse Transform Sampling routine for the Exponential models.

DyGyS.ensemble_Functions.IT_sampling_Gamma(random_array, zij, beta_0, phi, n_ensemble)

Inverse Transform Sampling routine for the Gamma models.

DyGyS.ensemble_Functions.IT_sampling_Lognormal(random_array, lnzij, gamma_0, n_ensemble)

Inverse Transform Sampling routine for the Lognormal models.

DyGyS.ensemble_Functions.IT_sampling_Pareto(random_array, shape, scale, n_ensemble)

Inverse Transform Sampling routine for the Pareto models.

DyGyS.ensemble_Functions.discrete_ensemble_matrix_directed(params, Wij, model, exogenous_variables, selection_variables=numpy.array, fixed_selection_params=numpy.array, n_ensemble=1000)

Generate ensemble of graphs for directed networks with discrete-valued weights

Parameters

• params (np.ndarray) – params after optimization

• Wij (np.ndarray) – weighted adjacency matrix

• model (str) – requested model for discrete-valued weights

• exogenous_variables (np.ndarray) – regressor matrix for the weighted gravity specification

• selection_variables (np.ndarray, optional) – topological regressor matrix for zero-inflated and L-C models. Defaults to np.array([]).

• fixed_selection_params (np.ndarray, optional) – fixed parameters for the topological stage for zero-inflated and L-C models. Defaults to np.array([]).

• n_ensemble (int, optional) – Number of graphs in the ensemble. Defaults to 1000.

Raises

TypeError – If model is not a discrete count data model or is not implemented.

Returns

Weighted adjacency matrices in the ensemble. Each column refers to each graph.

Return type

np.ndarray

DyGyS.ensemble_Functions.discrete_ensemble_matrix_undirected(params, Wij, model, exogenous_variables, selection_variables=numpy.array, fixed_selection_params=numpy.array, n_ensemble=1000)

Generate ensemble of graphs for undirected networks with discrete-valued weights

Parameters

• params (np.ndarray) – params after optimization

• Wij (np.ndarray) – weighted adjacency matrix

• model (str) – requested model for discrete-valued weights

• exogenous_variables (np.ndarray) – regressor matrix for the weighted gravity specification

• selection_variables (np.ndarray, optional) – topological regressor matrix for zero-inflated and L-C models. Defaults to np.array([]).

• fixed_selection_params (np.ndarray, optional) – fixed parameters for the topological stage for zero-inflated and L-C models. Defaults to np.array([]).

• n_ensemble (int, optional) – Number of graphs in the ensemble. Defaults to 1000.

Raises

TypeError – If model is not a discrete count data model or is not implemented.

Returns

Weighted adjacency matrices in the ensemble. Each column refers to each graph.

Return type

np.ndarray

DyGyS.ensemble_Functions.faster_ensemble_matrix_directed(params, Wij, model, exogenous_variables, selection_variables=numpy.array, fixed_selection_params=numpy.array, n_ensemble=1000)

Generate ensemble of graphs for directed networks with continuous-valued weights

Parameters

• params (np.ndarray) – params after optimization

• Wij (np.ndarray) – weighted adjacency matrix

• model (str) – requested model for discrete-valued weights

• exogenous_variables (np.ndarray) – regressor matrix for the weighted gravity specification

• selection_variables (np.ndarray, optional) – topological regressor matrix for zero-inflated and L-C models. Defaults to np.array([]).

• fixed_selection_params (np.ndarray, optional) – fixed parameters for the topological stage for zero-inflated and L-C models. Defaults to np.array([]).

• n_ensemble (int, optional) – Number of graphs in the ensemble. Defaults to 1000.

Raises

TypeError – If model is not a discrete count data model or is not implemented.

Returns

Weighted adjacency matrices in the ensemble. Each column refers to each graph.

Return type

np.ndarray

DyGyS.ensemble_Functions.faster_ensemble_matrix_undirected(params, Wij, model, exogenous_variables, selection_variables=numpy.array, fixed_selection_params=numpy.array, n_ensemble=1000)

Generate ensemble of graphs for undirected networks with continuous-valued weights

Parameters

• params (np.ndarray) – params after optimization

• Wij (np.ndarray) – weighted adjacency matrix

• model (str) – requested model for discrete-valued weights

• exogenous_variables (np.ndarray) – regressor matrix for the weighted gravity specification

• selection_variables (np.ndarray, optional) – topological regressor matrix for zero-inflated and L-C models. Defaults to np.array([]).

• fixed_selection_params (np.ndarray, optional) – fixed parameters for the topological stage for zero-inflated and L-C models. Defaults to np.array([]).

• n_ensemble (int, optional) – Number of graphs in the ensemble. Defaults to 1000.

Raises

TypeError – If model is not a discrete count data model or is not implemented.

Returns

Weighted adjacency matrices in the ensemble. Each column refers to each graph.

Return type

np.ndarray

Network Statistics Functions

DyGyS.netstats_Functions.ACC(adj_emp, adj_ens)

Computes Accuracy given empirical and expected binary adjacency matrices.

DyGyS.netstats_Functions.ACC_ensemble(pij_mat, aij_emp, n_ensemble=1000, percentiles=(2.5, 97.5))

Computes various statistics for Accuracy in the Graph Ensemble.

It returns the ensemble average, standard deviation, percentiles and array for ACC.

Parameters

• pij_mat (np.ndarray) – expected binary adjacency matrix

• aij_emp (np.ndarray) – empirical binary adjacency matrix

• n_ensemble (int, optional) – Number of graphs in the ensemble. Defaults to 1000.

• percentiles (tuple, optional) – Percentiles to compute. Defaults to (2.5,97.5).

DyGyS.netstats_Functions.AIC(ll, nparams)

Computes Akaike Measure given log-likelihood value and number of free parameters

DyGyS.netstats_Functions.BACC(adj_emp, adj_ens)

Computes Balanced Accuracy given empirical and expected binary adjacency matrices.

DyGyS.netstats_Functions.BACC_ensemble(pij_mat, aij_emp, n_ensemble=1000, percentiles=(2.5, 97.5))

Computes various statistics for Balanced Accuracy in the Graph Ensemble.

It returns the ensemble average, standard deviation, percentiles and array for BACC.

Parameters

• pij_mat (np.ndarray) – expected binary adjacency matrix

• aij_emp (np.ndarray) – empirical binary adjacency matrix

• n_ensemble (int, optional) – Number of graphs in the ensemble. Defaults to 1000.

• percentiles (tuple, optional) – Percentiles to compute. Defaults to (2.5,97.5).

DyGyS.netstats_Functions.BIC(ll, nparams, nobs)

Computes BIC Measure given log-likelihood value, number of free parameters and number of observations.

DyGyS.netstats_Functions.F1_score(adj_emp, adj_ens)

Computes F1 Score given empirical and expected binary adjacency matrices.

DyGyS.netstats_Functions.F1_score_ensemble(pij_mat, aij_emp, n_ensemble=1000, percentiles=(2.5, 97.5))

Computes various statistics for F1 Score in the Graph Ensemble.

It returns the ensemble average, standard deviation, percentiles and array for F1score.

Parameters

• pij_mat (np.ndarray) – expected binary adjacency matrix

• aij_emp (np.ndarray) – empirical binary adjacency matrix

• n_ensemble (int, optional) – Number of graphs in the ensemble. Defaults to 1000.

• percentiles (tuple, optional) – Percentiles to compute. Defaults to (2.5,97.5).

DyGyS.netstats_Functions.PPV(adj_emp, adj_ens)

Computes Precision given empirical and expected binary adjacency matrices.

DyGyS.netstats_Functions.PPV_ensemble(pij_mat, aij_emp, n_ensemble=1000, percentiles=(2.5, 97.5))

Computes various statistics for Precision in the Graph Ensemble.

It returns the ensemble average, standard deviation, percentiles and array for PPV.

param pij_mat

expected binary adjacency matrix

type pij_mat

np.ndarray

param aij_emp

empirical binary adjacency matrix

type aij_emp

np.ndarray

param n_ensemble

Number of graphs in the ensemble. Defaults to 1000.

type n_ensemble

int, optional

param percentiles

Percentiles to compute. Defaults to (2.5,97.5).

type percentiles

tuple, optional

DyGyS.netstats_Functions.SPC(adj_emp, adj_ens)

Computes Specificity given empirical and expected binary adjacency matrices.

DyGyS.netstats_Functions.SPC_ensemble(pij_mat, aij_emp, n_ensemble=1000, percentiles=(2.5, 97.5))

Computes various statistics for Specificity in the Graph Ensemble.

It returns the ensemble average, standard deviation, percentiles and array for SPC.

Parameters

• pij_mat (np.ndarray) – expected binary adjacency matrix

• aij_emp (np.ndarray) – empirical binary adjacency matrix

• n_ensemble (int, optional) – Number of graphs in the ensemble. Defaults to 1000.

• percentiles (tuple, optional) – Percentiles to compute. Defaults to (2.5,97.5).

DyGyS.netstats_Functions.TPR(adj_emp, adj_ens)

Computes True Positive Rate given empirical and expected binary adjacency matrices.

DyGyS.netstats_Functions.TPR_ensemble(pij_mat, aij_emp, n_ensemble=1000, percentiles=(2.5, 97.5))

Computes various statistics for True Positive Rate in the Graph Ensemble. It returns the ensemble average, standard deviation, percentiles and array for TPR.

Parameters

• pij_mat (np.ndarray) – expected binary adjacency matrix

• aij_emp (np.ndarray) – empirical binary adjacency matrix

• n_ensemble (int, optional) – Number of graphs in the ensemble. Defaults to 1000.

• percentiles (tuple, optional) – Percentiles to compute. Defaults to (2.5,97.5).

DyGyS.netstats_Functions.annd_ensemble(w_mat_ensemble, percentiles=(2.5, 97.5))

Computes various statistics for average neighbor degree centrality in the Graph Ensemble, consisting of ensemble average, standard deviation, percentiles and ensemble distribution.

Params w_mat_ensemble

weighted adjacency matrices for the Graph Ensemble

Params percentiles

percentages for percentile CI extracted from the ensemble. Defaults to (2.5,97.5).

DyGyS.netstats_Functions.anns_ensemble(w_mat_ensemble, percentiles=(2.5, 97.5))

Computes various statistics for average neighbor strength centrality in the Graph Ensemble, consisting of ensemble average, standard deviation, percentiles and ensemble distribution.

Params w_mat_ensemble

weighted adjacency matrices for the Graph Ensemble

Params percentiles

percentages for percentile CI extracted from the ensemble. Defaults to (2.5,97.5).

DyGyS.netstats_Functions.binarize(input)

Return binary adjacency matrix from weighted adjacency matrix.

DyGyS.netstats_Functions.clust_ensemble(w_mat_ensemble, percentiles=(2.5, 97.5))

Computes various statistics for binary clustering coefficient centrality in the Graph Ensemble, consisting of ensemble average, standard deviation, percentiles and ensemble distribution.

Params w_mat_ensemble

weighted adjacency matrices for the Graph Ensemble

Params percentiles

percentages for percentile CI extracted from the ensemble. Defaults to (2.5,97.5).

DyGyS.netstats_Functions.clust_single_fast(adj)

Computes binary clustering coefficient(cycle-type).

DyGyS.netstats_Functions.clust_w_single_fast(w_adj, adj)

Computes linear weighted clustering coefficient (cycle type).

DyGyS.netstats_Functions.cw_ensemble(w_mat_ensemble, percentiles=(2.5, 97.5))

Computes various statistics for (linear) weighted clustering coefficient centrality in the Graph Ensemble, consisting of ensemble average, standard deviation, percentiles and ensemble distribution.

Params w_mat_ensemble

weighted adjacency matrices for the Graph Ensemble

Params percentiles

percentages for percentile CI extracted from the ensemble. Defaults to (2.5,97.5).

DyGyS.netstats_Functions.deg(adj)

Compute (out-)degree centrality for (Directed)Undirected Networks.

DyGyS.netstats_Functions.deg_in(adj)

Compute in-degree centrality for Directed Networks.

DyGyS.netstats_Functions.degree_ensemble(w_mat_ensemble, percentiles=(2.5, 97.5))

Computes various statistics for (out-)degree centrality in the Graph Ensemble, consisting of ensemble average, standard deviation, percentiles and ensemble distribution.

Params w_mat_ensemble

weighted adjacency matrices for the Graph Ensemble

Params percentiles

percentages for percentile CI extracted from the ensemble. Defaults to (2.5,97.5).

DyGyS.netstats_Functions.degree_in_ensemble(w_mat_ensemble, percentiles=(2.5, 97.5))

Computes various statistics for in-degree centrality in the Graph Ensemble, consisting of ensemble average, standard deviation, percentiles and ensemble distribution.

Params w_mat_ensemble

weighted adjacency matrices for the Graph Ensemble

Params percentiles

percentages for percentile CI extracted from the ensemble. Defaults to (2.5,97.5).

DyGyS.netstats_Functions.ensemble_coverage(w_mat_ensemble, wij_emp, percentiles=(2.5, 97.5), stats=['degree', 'annd', 'clust', 'strength', 'anns', 'cw'])

Computes Statistic Reproduction Accuracy for the network statistics in the stats-list

Parameters

• w_mat_ensemble (np.ndarray) – weighted adjacency matrices in the graph ensemble

• wij_emp (np.ndarray) – empirical weighted adjacency matrix

• percentiles (tuple, optional) – percentages for ensemble percentiles. Defaults to (2.5,97.5).

• stats (list, optional) – list of statistics to compute. Defaults to [“degree”,”annd”,”clust”,”strength”,”anns”,”cw”].

Returns

list of reproduction accuracies for the network statistics in input list stats.

Return type

list

DyGyS.netstats_Functions.flatten(input)

Flatten numpy 2-D matrix to numpy 1-D array.

DyGyS.netstats_Functions.is_symmetric(input)

Check if weighted adjacency matrix is symmetric.

DyGyS.netstats_Functions.knn_single(adj)

Compute (out/out)average neighbor degree.

DyGyS.netstats_Functions.matrixate(input)

Turns 1-D numpy array into a numpy 2-D matrix.

DyGyS.netstats_Functions.pij_matrix_directed(params, method, Wij, selection_variables=numpy.array, exogenous_variables=numpy.array, fixed_selection_params=numpy.array)

Computes expected binary adjacency matrix according to model of choice for Directed networks.

Parameters

• params (np.ndarray) – params after optimization

• Wij (np.ndarray) – weighted adjacency matrix

• model (str) – requested model for discrete-valued weights

• exogenous_variables (np.ndarray) – regressor matrix for the weighted gravity specification

• selection_variables (np.ndarray, optional) – topological regressor matrix for zero-inflated and L-C models. Defaults to np.array([]).

• fixed_selection_params (np.ndarray, optional) – fixed parameters for the topological stage for zero-inflated and L-C models. Defaults to np.array([]).

• n_ensemble (int, optional) – Number of graphs in the ensemble. Defaults to 1000.

Returns

topological expected matrix in 1-D form

Return type

np.ndarray

DyGyS.netstats_Functions.pij_matrix_undirected(params, method, Wij, selection_variables=numpy.array, exogenous_variables=numpy.array, fixed_selection_params=numpy.array)

Computes expected binary adjacency matrix according to model of choice for Undirected networks.

Parameters

• params (np.ndarray) – params after optimization

• Wij (np.ndarray) – weighted adjacency matrix

• model (str) – requested model for discrete-valued weights

• exogenous_variables (np.ndarray) – regressor matrix for the weighted gravity specification

• selection_variables (np.ndarray, optional) – topological regressor matrix for zero-inflated and L-C models. Defaults to np.array([]).

• fixed_selection_params (np.ndarray, optional) – fixed parameters for the topological stage for zero-inflated and L-C models. Defaults to np.array([]).

• n_ensemble (int, optional) – Number of graphs in the ensemble. Defaults to 1000.

Returns

topological expected matrix in 1-D form

Return type

np.ndarray

DyGyS.netstats_Functions.st_ensemble(w_mat_ensemble, percentiles=(2.5, 97.5))

Computes various statistics for (out-)strength centrality in the Graph Ensemble, consisting of ensemble average, standard deviation, percentiles and ensemble distribution.

Params w_mat_ensemble

weighted adjacency matrices for the Graph Ensemble

Params percentiles

percentages for percentile CI extracted from the ensemble. Defaults to (2.5,97.5).

DyGyS.netstats_Functions.st_in_ensemble(w_mat_ensemble, percentiles=(2.5, 97.5))

Computes various statistics for in-strength centrality in the Graph Ensemble, consisting of ensemble average, standard deviation, percentiles and ensemble distribution.

Params w_mat_ensemble

weighted adjacency matrices for the Graph Ensemble

Params percentiles

percentages for percentile CI extracted from the ensemble. Defaults to (2.5,97.5).

DyGyS.netstats_Functions.stnn_single(w_adj, adj)

Computes (out/out) average neighbor strength.

DyGyS.netstats_Functions.strength(w_adj)

Computes (out-)strength sequence for (Directed)Undirected networks

DyGyS.netstats_Functions.strength_in(w_adj)

Computes in-strength sequence

DyGyS.netstats_Functions.symmetrize(input)

Symmetrize weighted adjacency matrix using the average between $$w_{ij}$$ and $$w_{ji}$$.

DyGyS.netstats_Functions.weighted_coverage(w_mat_ensemble, wij_emp, percentiles=(2.5, 97.5))

Computes Reproduction Accuracy for the weights

Parameters

• w_mat_ensemble (np.ndarray) – weighted adjacency matrices in the graph ensemble

• wij_emp (np.ndarray) – empirical weighted adjacency matrix

• percentiles (tuple, optional) – percentages for ensemble percentiles. Defaults to (2.5,97.5).

Returns

list of reproduction accuracies for the weights.

Return type

list

Solver Functions

DyGyS.solver_Functions.binarize(input)

Computes binary adjacency matrix from weighted adjacency matrix.

DyGyS.solver_Functions.solver(model, Wij, selection_variables, exogenous_variables, fixed_selection_params=numpy.array, tol=1e-05, use_guess=numpy.array, verbose=False, print_steps=1, maxiter=20)

Solves chosen model using scipy.optimize and scipy.least_squares routines.

Parameters

• model (str) – chosen model

• Wij (np,ndarray) – weighted adjacency matrix

• selection_variables (np.ndarray) – regressor matrix for the topological optimization of Zero-Inflated and L-constrained Conditional Models.

• exogenous_variables (np.ndarray) – regressor matrix for the weighted optimization

• fixed_selection_variables (np.ndarray) – fixed parameters for the topological optimization of Zero-Inflated and L-constrained Conditional Models. Defaults to np.array([1.00000,1.0000,0.0000]).

• tol (float, optional) – tolerance for optimization. Defaults to 1e-5.

• use_guess (np.ndarray, optional) – optional starter guess for the optimization process. Defaults to np.array([]).

• verbose (bool, optional) – True if you want to print iteration values of infinite norm. Defaults to False.

• print_steps (int, optional) – If verbose is True, you decide after how many steps you print on the screen. Defaults to 1.

• maxiter (int, optional) – Maxiter for optimization process. Defaults to 10.

Raises

TypeError – If chosen model is not correctly written or not implemented. See self.implemented_models to see available models.

Returns

estimated model solution

Return type

np.ndarray

Criterion Functions for Conditional MaxEnt Models

DyGyS.ll_Functions_conditional.alpha_estimate_CLognormal(params_exog, Wij, exogenous_variables)

Computes an approximate estimate for the last parameter of the Lognormal model given the others.

DyGyS.ll_Functions_conditional.binarize(input)

Computes binary adjacency matrix from weighted matrix.

DyGyS.ll_Functions_conditional.hess_BCM(params, Wij)

Computes opposite of the hessian for Undirected Binary Configuration Model

DyGyS.ll_Functions_conditional.hess_CExp(params, Wij, exogenous_variables)

Computes the opposite of the hessian for the weighted part of the Conditional Exponential model

DyGyS.ll_Functions_conditional.hess_CGeom(params, Wij, exogenous_variables)

Computes the opposite of the hessian for the weighted part of the Conditional Geometric model

DyGyS.ll_Functions_conditional.hess_DBCM(params, Wij)

Computes opposite of the hessian for Directed Binary Configuration Model

DyGyS.ll_Functions_conditional.jac_BCM(params, Wij)

Computes opposite of the jacobian for Undirected Binary Configuration Model

DyGyS.ll_Functions_conditional.jac_CExp(params, Wij, exogenous_variables)

Computes the opposite of the jacobian for the weighted part of the Conditional Exponential model

DyGyS.ll_Functions_conditional.jac_CGamma(params, Wij, exogenous_variables)

Computes the opposite of the jacobian for the weighted part of the Conditional Gamma model

DyGyS.ll_Functions_conditional.jac_CGeom(params, Wij, exogenous_variables)

Computes the opposite of the jacobian for the weighted part of the Conditional Geometric model

DyGyS.ll_Functions_conditional.jac_CLognormal(params, Wij, exogenous_variables)

Computes the opposite of the jacobian for the weighted part of the Conditional Lognormal model

DyGyS.ll_Functions_conditional.jac_CPareto(params_exog, Wij, exogenous_variables)

Computes the opposite of the jacobian for the weighted part of the Conditional Pareto model

DyGyS.ll_Functions_conditional.jac_DBCM(params, Wij)

Computes opposite of the jacobian for Directed Binary Configuration Model

DyGyS.ll_Functions_conditional.jac_logit(params, Wij, selection_variables, fixed_selection_params=numpy.array)

Computes opposite of the jacobian for Logit model

DyGyS.ll_Functions_conditional.ll_BCM(params, Wij)

Computes opposite of the log-likelihood for Undirected Binary Configuration Model

DyGyS.ll_Functions_conditional.ll_CExp(params, Wij, exogenous_variables)

Computes the opposite of the log-likelihood for the weighted part of the Conditional Exponential model

DyGyS.ll_Functions_conditional.ll_CGamma(params, Wij, exogenous_variables)

Computes the opposite of the log-likelihood for the weighted part of the Conditional Gamma model

DyGyS.ll_Functions_conditional.ll_CGeom(params, Wij, exogenous_variables)

Computes the opposite of the log-likelihood for the weighted part of the Conditional Geometric model

DyGyS.ll_Functions_conditional.ll_CLognormal(params, Wij, exogenous_variables)

Computes the opposite of the log-likelihood for the weighted part of the Conditional Lognormal model

DyGyS.ll_Functions_conditional.ll_CPareto(params_exog, Wij, exogenous_variables)

Computes the opposite of the log-likelihood for the weighted part of the Conditional Pareto model

DyGyS.ll_Functions_conditional.ll_DBCM(params, Wij)

Computes opposite of the log-likelihood for Directed Binary Configuration Model

DyGyS.ll_Functions_conditional.ll_logit(params, Wij, selection_variables, fixed_selection_params=numpy.array)

Computes opposite of the log-likelihood for Logit model

Criterion Functions for Integrated MaxEnt Models

DyGyS.ll_Functions_integrated.binarize(input)

Computes binary adjacency matrix from weighted matrix.

DyGyS.ll_Functions_integrated.hess_LIExp(params, Wij, exogenous_variables)

Computes the opposite of the hessian for the L-constrained Integrated Exponential model

DyGyS.ll_Functions_integrated.hess_LIGeom(params, Wij, exogenous_variables)

Computes the opposite of the hessian for the L-constrained Integrated Geometric model

DyGyS.ll_Functions_integrated.hess_kIExp_topological_undirected(theta_0, Wij, exogenous_variables, params_exog, b0)

Computes the opposite of the topological hessian for the k-constrained Integrated Exponential model for Undirected networks

DyGyS.ll_Functions_integrated.hess_kIExp_undirected(params, Wij, exogenous_variables)

Computes the opposite of the hessian for the k-constrained Integrated Exponential model for Undirected networks

DyGyS.ll_Functions_integrated.hess_kIGeom_topological_undirected(theta, Wij, exogenous_variables, params_exog, z_0)

Computes the opposite of the topological hessian for the k-constrained Integrated Geometric model for Undirected networks. Used in the solver

DyGyS.ll_Functions_integrated.hess_kIGeom_undirected(params, Wij, exogenous_variables)

Computes the opposite of the hessian for the k-constrained Integrated Geometric model for Undirected networks

DyGyS.ll_Functions_integrated.jac_LIExp(params, Wij, exogenous_variables)

Computes the opposite of the jacobian for the L-constrained Integrated Exponential model

DyGyS.ll_Functions_integrated.jac_LIGeom(params, Wij, exogenous_variables)

Computes the opposite of the jacobian for the L-constrained Integrated Geometric model

DyGyS.ll_Functions_integrated.jac_kIExp_directed(params, Wij, exogenous_variables)

Computes the opposite of the jacobian for the k-constrained Integrated Exponential model for Directed networks

DyGyS.ll_Functions_integrated.jac_kIExp_topological_directed(theta, Wij, exogenous_variables, params_exog, beta_0)

Computes the opposite of the topological jacobian for the k-constrained Integrated Exponential model for Directed networks

DyGyS.ll_Functions_integrated.jac_kIExp_topological_undirected(theta, Wij, exogenous_variables, params_exog, beta_0)

Computes the opposite of the topological jacobian for the k-constrained Integrated Exponential model for Undirected networks

DyGyS.ll_Functions_integrated.jac_kIExp_undirected(params, Wij, exogenous_variables)

Computes the opposite of the jacobian for the k-constrained Integrated Exponential model for Undirected networks

DyGyS.ll_Functions_integrated.jac_kIGeom_directed(params, Wij, exogenous_variables)

Computes the opposite of the jacobian for the k-constrained Integrated Geometric model for Directed networks

DyGyS.ll_Functions_integrated.jac_kIGeom_topological_directed(theta, Wij, exogenous_variables, params_exog, z_0)

Computes the opposite of the topological jacobian for the k-constrained Integrated Geometric model for Directed networks

DyGyS.ll_Functions_integrated.jac_kIGeom_topological_undirected(theta_i, Wij, exogenous_variables, params_exog, z_0)

Computes the opposite of the topological jacobian for the k-constrained Integrated Geometric model for Undirected networks. Used in the solver.

DyGyS.ll_Functions_integrated.jac_kIGeom_undirected(params, Wij, exogenous_variables)

Computes the opposite of the jacobian for the k-constrained Integrated Geometric model for Undirected networks

DyGyS.ll_Functions_integrated.ll_LIExp(params, Wij, exogenous_variables)

Computes the opposite of the log-likelihood for the L-constrained Integrated Exponential model

DyGyS.ll_Functions_integrated.ll_LIExp_binary(params, Wij, exogenous_variables)

Computes the opposite of the binary log-likelihood for the L-constrained Integrated Exponential model

DyGyS.ll_Functions_integrated.ll_LIGeom(params, Wij, exogenous_variables)

Computes the opposite of the log-likelihood for the L-constrained Integrated Geometric model

DyGyS.ll_Functions_integrated.ll_LIGeom_binary(params, Wij, exogenous_variables)

Computes the opposite of the binary log-likelihood for the L-constrained Integrated Geometric model

DyGyS.ll_Functions_integrated.ll_kIExp_binary_directed(params, Wij, exogenous_variables)

Computes the opposite of the binary log-likelihood for the k-constrained Integrated Exponential model for Directed networks

DyGyS.ll_Functions_integrated.ll_kIExp_binary_undirected(params, Wij, exogenous_variables)

Computes the opposite of the binary log-likelihood for the k-constrained Integrated Exponential model for Undirected networks

DyGyS.ll_Functions_integrated.ll_kIExp_directed(params, Wij, exogenous_variables)

Computes the opposite of the log-likelihood for the k-constrained Integrated Exponential model for Directed networks

DyGyS.ll_Functions_integrated.ll_kIExp_undirected(params, Wij, exogenous_variables)

Computes the opposite of the log-likelihood for the k-constrained Integrated Exponential model for Undirected networks

DyGyS.ll_Functions_integrated.ll_kIGeom_binary_directed(params, Wij, exogenous_variables)

Computes the opposite of the binary log-likelihood for the k-constrained Integrated Geometric model for Directed networks

DyGyS.ll_Functions_integrated.ll_kIGeom_binary_undirected(params, Wij, exogenous_variables)

Computes the opposite of the binary log-likelihood for the k-constrained Integrated Geometric model for Undirected networks

DyGyS.ll_Functions_integrated.ll_kIGeom_directed(params, Wij, exogenous_variables)

Computes the opposite of the log-likelihood for the k-constrained Integrated Geometric model for Directed networks

DyGyS.ll_Functions_integrated.ll_kIGeom_undirected(params, Wij, exogenous_variables)

Computes the opposite of the log-likelihood for the k-constrained Integrated Geometric model for Undirected networks

Criterion Functions for Econometric Models

DyGyS.ll_Functions_econometrics.binarize(input)

Computes binary adjacency matrix from weighted matrix.

DyGyS.ll_Functions_econometrics.guess_constant_parameter(Wij, exogenous_variables)

Estimate approximate first parameter for the solver of Poisson model

DyGyS.ll_Functions_econometrics.jac_NB2(params, Wij, exogenous_variables)

Computes opposite of the jacobian for Negative Binomial model

DyGyS.ll_Functions_econometrics.jac_POIS(params, Wij, exogenous_variables)

Computes opposite of the jacobian for Poisson model

DyGyS.ll_Functions_econometrics.jac_ZINB(params, Wij, selection_variables, exogenous_variables, fixed_selection_params=numpy.array)

Compute the opposite of the jacobian for Zero-Inflated Negative Binomial model

DyGyS.ll_Functions_econometrics.jac_ZIP(params, Wij, selection_variables, exogenous_variables, fixed_selection_params=numpy.array)

Compute the opposite of the jacobian for Zero-Inflated Poisson model

DyGyS.ll_Functions_econometrics.ll_NB2(params, Wij, exogenous_variables)

Computes opposite of the log-likelihood for Negative Binomial model

DyGyS.ll_Functions_econometrics.ll_NB2_binary(params, Wij, exogenous_variables)

Computes opposite of the binary log-likelihood for Negative Binomial model

DyGyS.ll_Functions_econometrics.ll_POIS(params, Wij, exogenous_variables)

Computes opposite of the log-likelihood for Poisson model

DyGyS.ll_Functions_econometrics.ll_POIS_binary(params, Wij, exogenous_variables)

Computes opposite of the binary log-likelihood for Poisson model

DyGyS.ll_Functions_econometrics.ll_ZINB(params, Wij, selection_variables, exogenous_variables, fixed_selection_params=numpy.array)

Compute the opposite of the log-likelihood for Zero-Inflated Negative Binomial model

DyGyS.ll_Functions_econometrics.ll_ZINB_binary(params, Wij, selection_variables, exogenous_variables, fixed_selection_params=numpy.array)

Compute the opposite of the binary log-likelihood for Zero-Inflated Negative Binomial model

DyGyS.ll_Functions_econometrics.ll_ZIP(params, Wij, selection_variables, exogenous_variables, fixed_selection_params=numpy.array)

Compute the opposite of the log-likelihood for Zero-Inflated Poisson model

DyGyS.ll_Functions_econometrics.ll_ZIP_binary(params, Wij, selection_variables, exogenous_variables, fixed_selection_params=numpy.array)

Compute the opposite of the binary log-likelihood for Zero-Inflated Poisson model