Degree matrix and volume of a graph

Formula: D = diag(d_1, ..., d_n), d_v = sum_u A_uv; vol(G) = sum_v d_v

Usage

Degmat(Adj)

Arguments

Adj

Symmetric adjacency matrix with a zero diagonal; entries may be 0/1 or non-negative edge weights.

Value

List with degrees, D, volume, n.

References

Chung, F. (1997), Spectral Graph Theory, CBMS Regional Conference Series in Mathematics 92, American Mathematical Society, is this package's primary book and is NOT in the reference library, so it could not be read. The conventions below were taken instead from the author's own survey, Chung, F., Four proofs for the Cheeger inequality and graph partition algorithms, Proceedings of ICCM 2007 Vol. II pp. 1-4, Sect. 2 (Preliminaries), which restates them in her notation. D is the diagonal degree matrix; vol(S) = sum over v in S of d_v, so vol(G) is the sum of all degrees, which is twice the number of edges for an unweighted graph.

Examples

Degmat(Adj = 5L)
#> $degrees
#> [1] 5
#> 
#> $D
#>      [,1]
#> [1,]    5
#> 
#> $volume
#> [1] 5
#> 
#> $n
#> [1] 1
#> 
#> $method
#> [1] "Degree matrix and graph volume"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"