networkanalysis.ergm#

This module manages exponential random graph models (ERGMs).

Functions

apl(mple, mle, statscomp, graph[, ngraphs, ...])

Compute the adjusted pseudolikelihood function of a graph.

ml(graph, statscomp[, init, ngraphs, ...])

Compute the maximum likelihood estimator.

mpl(graph, statscomp[, return_statscomp])

Compute the maximum pseudolikelihood estimator.

pl(graph, param, statscomp[, return_statscomp])

Compute the pseudolikelihood of a graph.

simulate(ngraphs, param, stats_comp, init[, ...])

Simulate ngraphs graphs with respect to the param and the sufficient statistics.
networkanalysis.ergm.apl(mple, mle, statscomp, graph, ngraphs=500, burnin=500, thin=5, return_statscomp=False)#

Compute the adjusted pseudolikelihood function of a graph.

Parameters:

  • mple (ndarray) – The maximum pseudolikelihood estimator.

  • mle (ndarray) – The maximum likelihood estimator.

  • statscomp (StatsComp | CachedStatsComp) – The function that computes the sufficient statistics.

  • graph (Graph) – The observed graph.

  • ngraphs (int, optional) – The number of graphs to simulate. Defaults to 500.

  • burnin (int, optional) – The number of iterations to discard. Defaults to 500.

  • thin (int, optional) – The thinning parameter. Defaults to 5.

  • return_statscomp (bool, optional) – Whether to return the function that computes the sufficient statistics. Defaults to False.

Returns:

  • The adjusted pseudolikelihood function with respect to the observed

    graph.

  • The statistics computer if return_statscomp is True.

Return type:

tuple[Callable[[numpy.ndarray], float], StatsComp | CachedStatsComp]

networkanalysis.ergm.ml(graph, statscomp, init=None, ngraphs=500, burnin=500, thin=5, bound=0.1, tol=1e-05, maxiter=50, return_statscomp=False)#

Compute the maximum likelihood estimator.

Parameters:

  • graph (Graph) – The graph to compute the estimator.

  • statscomp (StatsComp | CachedStatsComp) – The function that computes the sufficient statistics.

  • init (ndarray, optional) – The initial parameter to start the optimization. If None, the maximum pseudolikelihood estimator is used. Defaults to None.

  • ngraphs (int, optional) – The number of graphs to use when using simulate. Defaults to 500.

  • burnin (int, optional) – The number of graphs to discard when using simulate. Defaults to 500.

  • thin (int, optional) – The thinning parameter when using simulate. Defaults to 5.

  • bound (float, optional) – The bound for the optimization. Defaults to 1e-1.

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

  • maxiter (int, optional) – The maximum number of iterations for the current two-phases algorithm. Defaults to 50.

  • return_statscomp (bool, optional) – Whether to return the function that computes the sufficient statistics. Defaults to False.

Returns:

The maximum likelihood estimator.

Return type:

tuple[ndarray, StatsComp | CachedStatsComp]

networkanalysis.ergm.mpl(graph, statscomp, return_statscomp=False)#

Compute the maximum pseudolikelihood estimator.

Parameters:

  • graph (Graph) – The observed graph.

  • statscomp (StatsComp | CachedStatsComp) – The statistics computer.

  • return_statscomp (bool, optional) – Whether to return the function that computes the sufficient statistics. Defaults to False.

Returns:

  • The maximum pseudolikelihood estimator.

  • The statistics computer if return_statscomp is True.

Return type:

tuple[ndarray, StatsComp | CachedStatsComp]

networkanalysis.ergm.pl(graph, param, statscomp, return_statscomp=False)#

Compute the pseudolikelihood of a graph.

Parameters:

  • graph (Graph) – The graph.

  • param (ndarray) – The parameter.

  • statscomp (StatsComp | CachedStatsComp) – The function that computes the sufficient statistics.

  • return_statscomp (bool, optional) – Whether to return the function that computes the sufficient statistics. Defaults to False.

Returns:

  • The pseudolikelihood of the graph.

  • The statistics computer if return_statscomp is True.

Return type:

tuple[ndarray, StatsComp | CachedStatsComp]

networkanalysis.ergm.simulate(ngraphs, param, stats_comp, init, burnin=0, thin=1, summary=False, warn=None, return_statscomp=False)#

Simulate ngraphs graphs with respect to the param and the sufficient statistics.

Parameters:

  • ngraphs (int) – The number of graphs to simulate.

  • param (ndarray) – The parameter of the model.

  • stats_comp (StatsComp | CachedStatsComp) – The sufficient statistics computer.

  • init (Graph, optional) – The initial graph to start the chain, or the number of nodes. If none is given, then a random graph is used.

  • burnin (int, optional) – The number of graphs to burn. If none is given, then no graphs will be burned. Defaults to 0.

  • thin (int, optional) – The thinning factor. Defaults to 1.

  • summary (bool, optional) – A flag for requesting to collect information about the chain such as the acceptance rate. Defaults to False.

  • warn (int, optional) – If an integer passed, then a warning is thrown if the graphs are near-empty or near-complete for this number of interation. Defaults to None.

  • return_statscomp (bool, optional) – A flag for requesting to return the sufficient statistics computer. Defaults to False.

Returns:

  • The simulated graphs.

  • A summary of the Markov chain used if summary is True.

  • The statistics computer if return_statistics is True.

Return type:

tuple[list[Graph], dict, StatsComp | CachedStatsComp]