# Posterior Distribution of Edge Weights of a Reconstructed Network

Dear Tiago,

We wish to use the Network Reconstruction module to obtain both the probability of the edges between any pair of nodes of an undirected graph as well as the posterior distribution of the edge weights following the reconstruction.

We have followed your online tutorial to obtain the former (u.ep.eprob), but are wondering if it is possible to also obtain a posterior distribution of a ‘reconstructed’ edge weight, based on the EdgePropertyMap ‘x’ (e.g. in MixedMeasuredBlockState) for positive occurrence?

Any help would be much appreciated!

Best wishes,
Michael

You’re looking for the function `collect_marginal_multigraph()`: graph_tool.inference.MeasuredBlockState — graph-tool 2.56 documentation

Dear Tiago,

Thank you for your prompt and helpful reply. We have taken the time to familiarise ourselves with the ‘collect_marginal_multigraph’ method and would like to clarify some points with you:

1. Our understanding is that the inferred edge weights (‘w’) and their respective counts (‘wcount’) are determined solely based on the measured, covariate-free multigraph, as well as the specified parameters ‘x’ and ‘n’ when applying one of the network reconstruction algorithms (e.g., MeasuredBlockState). After the MCMC run, we can retrieve the edge multiplicities and counts, allowing us to calculate the average multiplicity (‘ew’). However, we are unsure about the treatment of weighted multigraphs that include edge covariates. Do the posterior samples from the inferred edge weights distribution take into account the original covariates? If not, is there a principled way to associate the inferred edge weights with the original covariates?

2. We are aware that the ‘collect_marginal’ method can provide us with edge probabilities (‘eprob’). Is it possible to collect both ‘eprob’ and ‘w’/‘wcount’ simultaneously?

We would be most grateful for your guidance!
Best wishes,

Michael

Dear Michael,

At the moment graph-tool does not include support for measured/uncertain graphs with edge covariates. For that, it would be needed to establish an error model for the covariates.

To obtain eprob and w/wcount you need keep two separate marginals graphs.

Best,
Tiago

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Many thanks for clarifying, very helpful.

Best wishes,
Michael