Combinatorial (unnormalised) Laplacian of a weighted graph

rowsum must be zero to machine precision: the all-ones vector is always in the kernel.

Usage

Graphlap(W)

Arguments

W

Symmetric non-negative weight matrix.

Value

List with L, degree, rowsum, n.

Details

Formula: L(u, v) = d_v - w(v, v) if u = v, -w(u, v) if u ~ v, else 0

References

Chung (1997), Spectral Graph Theory, CBMS 92, Section 1.4, which generalises the Section 1.2 definition to weighted graphs with loops exactly as written above.

Examples

Graphlap(W = 5L)
#> $L
#>      [,1]
#> [1,]    0
#> 
#> $degree
#> [1] 5
#> 
#> $rowsum
#> [1] 0
#> 
#> $n
#> [1] 1
#> 
#> $method
#> [1] "Combinatorial Laplacian L = T - A"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"