# sdsm: The stochastic degree sequence model (sdsm) for backbone... In backbone: Extracts the Backbone from Weighted Graphs

## Description

'sdsm' computes the probability of edge weights being above or below the observed edge weights in a bipartite projection using the stochastic degree sequence model. Once computed, use `backbone.extract` to return the backbone matrix for a given alpha value.

## Usage

 `1` ```sdsm(B, method = "RefinedNormal", ...) ```

## Arguments

 `B` graph: An unweighted bipartite graph object of class matrix, sparse matrix, igraph, edgelist, or network object. Any rows and columns of the associated bipartite matrix that contain only zeros are automatically removed before computations. `method` string: Specifies the method of the Poisson Binomial distribution computation used by the "ppbinom" function in PoissonBinomial-Distribution. "RefinedNormal" gives quick, very accurate approximations, while "DivideFFT" gives the quickest exact computations. `...` optional arguments

## Details

The sdsm function compares an edge's observed weight in the projection `B*t(B)` to the distribution of weights expected in a projection obtained from a random bipartite network where both the row vertex degrees and column vertex degrees are approximately fixed. It uses the Bipartite Configuration Model bicm (Saracco et. al (2015, 2017)) to compute probabilities for the Poisson binomial distribution.

The "backbone" S3 class object returned is composed of two matrices, and a summary dataframe.

## Value

backbone, a list(positive, negative, summary). Here 'positive' is a matrix of probabilities of edge weights being equal to or above the observed value in the projection, 'negative' is a matrix of probabilities of edge weights being equal to or below the observed value in the projection, and 'summary' is a data frame summary of the inputted matrix and the model used including: class, model name, number of rows, number of columns, and running time.

## References

sdsm: Neal, Z. P. (2014). The backbone of bipartite projections: Inferring relationships from co-authorship, co-sponsorship, co-attendance, and other co-behaviors. Social Networks, 39, Elsevier: 84-97. doi: 10.1016/j.socnet.2014.06.001

bicm: Saracco, F., Straka, M. J., Clemente, R. D., Gabrielli, A., Caldarelli, G., & Squartini, T. (2017). Inferring monopartite projections of bipartite networks: An entropy-based approach. New Journal of Physics, 19(5), 053022. doi: 10.1088/1367-2630/aa6b38

bicm: Saracco, F., Di Clemente, R., Gabrielli, A., & Squartini, T. (2015). Randomizing bipartite networks: The case of the World Trade Web. Scientific Reports, 5(1), 10595. doi: 10.1038/srep10595

## Examples

 `1` ```sdsm_probs <- sdsm(davis) ```

### Example output

```Finding the distribution using SDSM with polytope model.
```

backbone documentation built on Sept. 18, 2021, 1:07 a.m.