laplacianFromA: Calculates the Laplacian associated to an adjacency matrix
In DEGraph: Two-sample tests on a graph

Description Usage Arguments Value Author(s) Examples

Calculates the Laplacian associated to an adjacency matrix.

1	laplacianFromA(A, k=1, ltype=c("meanInfluence", "normalized", "unnormalized", "totalInfluence"))

`A`	The adjacency matrix of the graph.
`k`	...
`ltype`	A `character` value specifying the type of Laplacian to be calculated. Defaults to meanInfluence.

A list containing the following components:

U: Eigenvectors of the graph Laplacian.
l: Eigenvalues of the graph Laplacian
kIdx: Multiplicity of '0' as eigenvalue.

Laurent Jacob, Pierre Neuvial and Sandrine Dudoit

library("KEGGgraph")
library("rrcov")

## Create a random graph
graph <- randomWAMGraph(nnodes=5, nedges=7, verbose=TRUE)
plot(graph)

## Retrieve its adjacency matrix
A <- graph@adjMat

## write it to KGML file
grPathname <- "randomWAMGraph.xml"
writeAdjacencyMatrix2KGML(A, pathname=grPathname, verbose=TRUE, overwrite=TRUE)

## read it from file
gr <- parseKGML2Graph(grPathname)

## Two examples of Laplacians from the same graph
lapMI <- laplacianFromA(A, ltype="meanInfluence")
print(lapMI)

lapN <- laplacianFromA(A, ltype="normalized")
print(lapN)

U <- lapN$U
p <- nrow(A)
sigma <- diag(p)/sqrt(p)

X <- twoSampleFromGraph(100, 120, shiftM2=1, sigma, U=U, k=3)

## T2
t <- T2.test(X$X1,X$X2)
str(t)

tu <- graph.T2.test(X$X1, X$X2, lfA=lapMI, k=3)
str(tu)

Loading required package: R.utils
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R.methodsS3 v1.7.1 (2016-02-15) successfully loaded. See ?R.methodsS3 for help.
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Attaching package: 'R.oo'

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Attaching package: 'R.utils'

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Loading required package: robustbase
Scalable Robust Estimators with High Breakdown Point (version 1.4-3)


Attaching package: 'rrcov'

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$U
           [,1]          [,2]       [,3]        [,4]          [,5]
[1,] -0.4472136  5.992908e-01  0.3193880  0.44496211 -3.753005e-01
[2,] -0.4472136  3.753005e-01 -0.5445805 -0.05858362  5.992908e-01
[3,] -0.4472136 -3.753005e-01 -0.5445805 -0.05858362 -5.992908e-01
[4,] -0.4472136 -2.220446e-16  0.4503850 -0.77275699 -1.443290e-15
[5,] -0.4472136 -5.992908e-01  0.3193880  0.44496211  3.753005e-01

$l
[1] 3.552714e-15 5.196613e-01 1.353491e+00 2.424287e+00 2.619228e+00

$kIdx
[1]  TRUE FALSE FALSE FALSE FALSE

$U
           [,1]          [,2]       [,3]          [,4]          [,5]
[1,] -0.3779645  5.869337e-01 -0.3273268  5.000000e-01 -3.943461e-01
[2,] -0.4629100  3.943461e-01  0.5345225 -7.216450e-16  5.869337e-01
[3,] -0.4629100 -3.943461e-01  0.5345225  4.718448e-16 -5.869337e-01
[4,] -0.5345225  5.551115e-17 -0.4629100 -7.071068e-01 -8.881784e-16
[5,] -0.3779645 -5.869337e-01 -0.3273268  5.000000e-01  3.943461e-01

$l
[1] 1.776357e-15 7.257081e-01 1.166667e+00 1.500000e+00 1.607625e+00

$kIdx
[1]  TRUE FALSE FALSE FALSE FALSE

Warning message:
In sqrt(shiftM2) * diff[1:k]/sqrt(rawShiftNorm) :
  Recycling array of length 1 in vector-array arithmetic is deprecated.
  Use c() or as.vector() instead.

List of 9
 $ statistic  : Named num [1:2] 44.66 8.77
  ..- attr(*, "names")= chr [1:2] "T2" "F"
 $ parameter  : Named num [1:2] 5 214
  ..- attr(*, "names")= chr [1:2] "df1" "df2"
 $ p.value    : num 1.39e-07
 $ conf.int   : NULL
 $ estimate   : num [1:2, 1:5] -2.28 -2.678 -0.897 -1.144 0.35 ...
  ..- attr(*, "dimnames")=List of 2
  .. ..$ : chr [1:2] "mean x-vector" "mean y-vector"
  .. ..$ : NULL
 $ null.value : NULL
 $ alternative: chr "true difference in mean vectors is not equal to (0,0,0,0,0)"
 $ method     : chr "Two-sample Hotelling test"
 $ data.name  : chr "X$X1 and X$X2"
 - attr(*, "class")= chr "htest"
List of 9
 $ statistic  : Named num [1:2] 43.3 14.3
  ..- attr(*, "names")= chr [1:2] "T2" "F"
 $ parameter  : Named num [1:2] 3 216
  ..- attr(*, "names")= chr [1:2] "df1" "df2"
 $ p.value    : num 1.57e-08
 $ conf.int   : NULL
 $ estimate   : num [1:2, 1:3] 1.586 2.106 -1.018 -1.253 -0.577 ...
  ..- attr(*, "dimnames")=List of 2
  .. ..$ : chr [1:2] "mean x-vector" "mean y-vector"
  .. ..$ : NULL
 $ null.value : NULL
 $ alternative: chr "true difference in mean vectors is not equal to (0,0,0)"
 $ method     : chr "Two-sample Hotelling test"
 $ data.name  : chr "X1 %*% U[, 1:rk, drop = FALSE] and X2 %*% U[, 1:rk, drop = FALSE]"
 - attr(*, "class")= chr "htest"