GetNormalizedLaplacianMatrix: Network normalized Laplacian

In manlius/muxViz: MuxViz - Visualization and Analysis of Multilayer Networks

Network normalized Laplacian

Description

Given an adjacency matrix A, the function builds the random walk (RW) normalised Laplacian I - D^{-1}A for a single-layer network. The RW normalised Laplacian is defined only for graphs without isolated nodes – due to the inversion of the diagonal matrix of degrees D^{-1}. Despite this, a (classical) random walk is still defined also in presence of isolates or nodes without out-going edges, simply setting the transition probability from those nodes outwards to be zero. Consequently we can extend the definition of the RW normalised Laplacian setting L_{ij} = 0 if k_i = 0 for all j.

Usage

GetNormalizedLaplacianMatrix(AdjacencyMatrix)

Arguments

AdjacencyMatrix

the adjacency matrix characterising the network

Value

Normalized Lapalacian Matrix

manlius/muxViz documentation built on March 1, 2023, 10:28 a.m.