graph_tool.inference.LatentClosureBlockState

class graph_tool.inference.LatentClosureBlockState(g, L=1, b=None, aE=nan, nested=True, state_args={}, g_orig=None, ew=None, ex=None, **kwargs)

Bases: LatentLayerBaseState

Inference state of the stochastic block model with latent triadic closure edges.

Parameters:

gGraph

Observed graph.

Lint (optional, default: 1)

Maximum number of triadic closure generations.

bVertexPropertyMap (optional, default: None)

Inital partition (or hierarchical partition nested=True).

aEfloat (optional, default: NaN)

Expected total number of edges used in prior. If NaN, a flat prior will be used instead.

nestedboolean (optional, default: True)

If True, a NestedBlockState will be used, otherwise BlockState.

state_argsdict (optional, default: {})

Arguments to be passed to NestedBlockState or BlockState.

g_origGraph (optional, default: None)

Original graph, if g is used to initialize differently from a graph with no triadic closure edges.

ewlist of EdgePropertyMap (optional, default: None)

List of edge property maps of g, containing the initial weights (counts) at each triadic generation.

exlist of EdgePropertyMap (optional, default: None)

List of edge property maps of g, each containing a list of integers with the ego graph memberships of every edge, for every triadic generation.

References

[peixoto-disentangling-2022]

Tiago P. Peixoto, “Disentangling homophily, community structure and triadic closure in networks”, Phys. Rev. X 12, 011004 (2022), DOI: 10.1103/PhysRevX.12.011004 [sci-hub, @tor], arXiv: 2101.02510

Methods

collect_marginal([gs])	Collect marginal inferred network during MCMC runs.
collect_marginal_multigraph([gs])	Collect marginal latent multigraphs during MCMC runs.
copy(**kwargs)	Return a copy of the state.
entropy([latent_edges, density])	Return the entropy, i.e. negative log-likelihood.
get_ec([ew])	Return edge property map with layer membership.
mcmc_sweep([r, multiflip])	Perform sweeps of a Metropolis-Hastings acceptance-rejection sampling MCMC to sample network partitions and latent edges.
multiflip_mcmc_sweep(**kwargs)	Alias for mcmc_sweep() with multiflip=True.
sample_graph([sample_sbm, canonical_sbm, ...])	Sample graph from inferred model.

collect_marginal(gs=None)

Collect marginal inferred network during MCMC runs.

Parameters:

glist of Graph (optional, default: None)

Previous marginal graphs.

Returns:

glist Graph

New list of marginal graphs, each with internal EdgePropertyMap "eprob", containing the marginal probabilities for each edge, as well as VertexPropertyMap "t", "m", "c", containing the average number of closures, open triads, and fraction of closed triads on each node.

Notes

The posterior marginal probability of an edge \((i,j)\) is defined as

\[\pi_{ij} = \sum_{\boldsymbol A}A_{ij}P(\boldsymbol A|\boldsymbol D)\]

where \(P(\boldsymbol A|\boldsymbol D)\) is the posterior probability given the data.

This function returns a list with the marginal graphs for every layer.

collect_marginal_multigraph(gs=None)

Collect marginal latent multigraphs during MCMC runs.

Parameters:

glist of Graph (optional, default: None)

Previous marginal multigraphs.

Returns:

glist of Graph

New marginal multigraphs, each with internal edge EdgePropertyMap "w" and "wcount", containing the edge multiplicities and their respective counts.

Notes

The mean posterior marginal multiplicity distribution of a multi-edge \((i,j)\) is defined as

\[\pi_{ij}(w) = \sum_{\boldsymbol G}\delta_{w,G_{ij}}P(\boldsymbol G|\boldsymbol D)\]

where \(P(\boldsymbol G|\boldsymbol D)\) is the posterior probability of a multigraph \(\boldsymbol G\) given the data.

This function returns a list with the marginal graphs for every layer.

copy(**kwargs)

Return a copy of the state.

entropy(latent_edges=True, density=True, **kwargs)

Return the entropy, i.e. negative log-likelihood.

get_ec(ew=None)

Return edge property map with layer membership.

mcmc_sweep(r=0.5, multiflip=True, **kwargs)

Perform sweeps of a Metropolis-Hastings acceptance-rejection sampling MCMC to sample network partitions and latent edges. The parameter r controls the probability with which edge move will be attempted, instead of partition moves. The remaining keyword parameters will be passed to mcmc_sweep() or multiflip_mcmc_sweep(), if multiflip=True.

multiflip_mcmc_sweep(**kwargs)

Alias for mcmc_sweep() with multiflip=True.

sample_graph(sample_sbm=True, canonical_sbm=False, sample_params=True, canonical_closure=True)

Sample graph from inferred model.

Parameters:

sample_sbmboolean (optional, default: True)

If True, the substrate network will be sampled anew from the SBM parameters. Otherwise, it will be the same as the current posterior state.

canonical_sbmboolean (optional, default: False)

If True, the canonical SBM will be used, otherwise the microcanonical SBM will be used.

sample_paramsbool (optional, default: True)

If True, and canonical_sbm == True the count parameters (edges between groups and node degrees) will be sampled from their posterior distribution conditioned on the actual state. Otherwise, their maximum-likelihood values will be used.

canonical_closureboolean (optional, default: True)

If True, the canonical version of triadic clousre will be used (i.e. conditioned on a probability), otherwise the microcanonical version will be used (i.e. conditional on the count number).

Returns:

ulist Graph

Sampled graph, with internal edge EdgePropertyMap "gen", containing the triadic generation of each edge.