marginal_multigraph_entropy#

graph_tool.inference.marginal_multigraph_entropy(g, ecount)[source]#

Compute the entropy of the marginal latent multigraph distribution.

Parameters:

gGraph

Marginal multigraph.

ecountEdgePropertyMap

Vector-valued edge property map containing the counts of edge multiplicities.

Returns:

ehEdgePropertyMap

Marginal entropy of edge multiplicities.

Notes

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

$${\pi }_{ij}(w)=\sum _{\mathit{G}}{\delta }_{w,G_{ij}}P(\mathit{G}|\mathit{D})$$

where $P(\mathit{G}|\mathit{D})$ is the posterior probability of a multigraph $\mathit{G}$ given the data.

The corresponding entropy is therefore given (in nats) by

$${\mathcal{S}}_{ij}=-\sum _w{\pi }_{ij}(w)\ln {\pi }_{ij}(w).$$