Computes the distribution of eigenvalues for the modified graph Laplacian of a phylogenetic tree, and several summary statistics of this distribution. The modified graph Laplacian of a phylogeny is given by the difference between its' distance matrix (e.g. all pairwise distances between all nodes), and the degree matrix (e.g. the diagonal matrix where each diagonal element represents the sum of branch lengths to all other nodes). Each row of the modified graph Laplacian sums to zero. For a tree with n tips, there are N = 2n-1 nodes, and hence the modified graph Laplacian is represented by a N x N matrix. Where RPANDA relies on the package igraph to calculate the modified graph Laplacian, the treestats package uses C++ to directly calculate the different entries in the matrix. This makes the treestats implementation slightly faster, although the bulk of computation occurs in estimating the eigen values, using the function eigen from base.
Value
list with five components: 1) eigenvalues the vector of eigen values, 2) principal_eigenvalue the largest eigenvalueof the spectral density distribution 3) asymmetry the skewness of the spectral density distribution 4) peak_height the largest y-axis valueof the spectral density distribution and 5) eigengap theposition ofthe largest difference between eigenvalues, giving the number of modalities in the tree.