gdim

Estimate Graph Dimension

https://github.com/rohelab/gdim

Repository

Estimate Graph Dimension

https://github.com/RoheLab/gdim/blob/main/

# gdim



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`gdim` estimates graph dimension using cross-validated eigenvalues, via
the graph-splitting technique developed in
. Theoretically, the method works by
computing a special type of cross-validated eigenvalue which follows a
simple central limit theorem. This allows users to perform hypothesis
tests on the rank of the graph.

## Installation

You can install `gdim` from CRAN with:

``` r
install.packages("gdim")

# to get the development version from GitHub:
install.packages("pak")
pak::pak("RoheLab/gdim")
```

## Example

`eigcv()` is the main function in `gdim`. The single required parameter
for the function is the maximum possible dimension, `k_max`.

In the following example, we generate a random graph from the stochastic
block model (SBM) with 1000 nodes and 5 blocks (as such, we would expect
the estimated graph dimension to be 5).

``` r
library(fastRG)
#> Loading required package: Matrix

B <- matrix(0.1, 5, 5)
diag(B) <- 0.3

model <- sbm(
  n = 1000,
  k = 5,
  B = B,
  expected_degree = 40,
  poisson_edges = FALSE,
  allow_self_loops = FALSE
)

A <- sample_sparse(model)
```

Here, `A` is the adjacency matrix.

Now, we call the `eigcv()` function with `k_max=10` to estimate graph
dimension.

``` r
library(gdim)

eigcv_result <- eigcv(A, k_max = 10)
#> 'as(, "dgCMatrix")' is deprecated.
#> Use 'as(., "generalMatrix")' instead.
#> See help("Deprecated") and help("Matrix-deprecated").
eigcv_result
#> Estimated graph dimension:    5
#> 
#> Number of bootstraps:         10
#> Edge splitting probabaility:  0.1
#> Significance level:       0.05
#> 
#>  ------------ Summary of Tests ------------
#>   k          z        pvals         padj
#>   1 59.7488180 2.220446e-16 2.220446e-15
#>   2 12.9094629 2.220446e-16 2.220446e-15
#>   3 11.8600427 2.220446e-16 2.220446e-15
#>   4 11.9412340 2.220446e-16 2.220446e-15
#>   5  9.0252520 2.220446e-16 2.220446e-15
#>   6 -0.8512008 8.026711e-01 1.000000e+00
#>   7 -0.8182195 7.933841e-01 1.000000e+00
#>   8 -0.9912649 8.392219e-01 1.000000e+00
#>   9 -0.9005808 8.160944e-01 1.000000e+00
#>  10 -1.1677953 8.785553e-01 1.000000e+00
```

In this example, `eigcv()` suggests `k=5`.

To visualize the result, use `plot()` which returns a `ggplot` object.
The function displays the test statistic (z score) for each hypothesized
graph dimension.

``` r
plot(eigcv_result)
```



## Reference

Chen, Fan, Sebastien Roch, Karl Rohe, and Shuqi Yu. Estimating Graph
Dimension with Cross-Validated Eigenvalues. ArXiv:2108.03336 \[Cs,
Math, Stat\], August 6, 2021. .

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