# plotMultiEigenvalues: plot eigenvalues 'plotMultiEigenvalues' plot eigenvalues to... In DCG: Data Cloud Geometry (DCG): Using Random Walks to Find Community Structure in Social Network Analysis

## Description

plot eigenvalues `plotMultiEigenvalues` plot eigenvalues to determine number of communities by finding the elbow point

## Usage

 ```1 2``` ```plotMultiEigenvalues(Ens_list, mfrow, mar = c(2, 2, 2, 2), line = -1.5, cex = 0.5, ...) ```

## Arguments

 `Ens_list` a list in which elements are numeric vectors representing eigenvalues. `mfrow` A vector of the form `c(nr, nc)` passed to `par`. `mar` plotting parameters with useful defaults (`par`) `line` plotting parameters with useful defaults (`par`) `cex` plotting parameters with useful defaults (`par`) `...` further plotting parameters

## Details

`plotMultiEigenvalues` plot multiple eigenvalue plots. The dark blue colored dots indicate eigenvalue greater than 0. Each of the ensemble matrices is decomposed into eigenvalues which is used to determine appropriate number of communities. Plotting out eigenvalues allow us to see where the elbow point is. The curve starting from the elbow point flatten out. The number of points above (excluding) the elbow point indicates number of communities.

`mfrow` determines the arrangement of multiple plots. It takes the form of `c(nr, nc)` with the first parameter being the number of rows and the second parameter being the number of columns. When deciding parameters for mfrow, one should take into considerations size of the plotting device and number of plots. For example, there are 20 plots, mfrow can be set to `c(4, 5)` or `c(2, 10)` depending on the size and shape of the plotting area.

## Value

a `pdf` file in the working directory containing all eigenvalue plots

## References

Fushing, H., & McAssey, M. P. (2010). Time, temperature, and data cloud geometry. Physical Review E, 82(6), 061110.

Chen, C., & Fushing, H. (2012). Multiscale community geometry in a network and its application. Physical Review E, 86(4), 041120.

Fushing, H., Wang, H., VanderWaal, K., McCowan, B., & Koehl, P. (2013). Multi-scale clustering by building a robust and self correcting ultrametric topology on data points. PloS one, 8(2), e56259.

`plotCLUSTERS`, `getEnsList`
 ``` 1 2 3 4 5 6 7 8 9 10 11``` ```symmetricMatrix <- as.symmetricAdjacencyMatrix(monkeyGrooming, weighted = TRUE, rule = "weak") Sim <- as.SimilarityMatrix(symmetricMatrix) temperatures <- temperatureSample(start = 0.01, end = 20, n = 20, method = 'random') ## Not run: # for illustration only. skip CRAN check because it ran forever. Ens_list <- getEnsList(Sim, temperatures, MaxIt = 1000, m = 5) ## End(Not run) plotMultiEigenvalues(Ens_list = Ens_list, mfrow = c(10, 2), mar = c(1, 1, 1, 1)) ```