#### Title

#### Document Type

Pre-Print

#### Publication Date

10-2017

#### Subjects

Directed graphs, Graph theory

#### Abstract

Let V = {1, · · · n} be a vertex set and S a non-negative row-stochastic matrix (i.e. rows sum to 1). V and S define a digraph G = G(V, S) and a directed graph Laplacian L as follows. If (S)ij > 0 (in what follows we will leave out the parentheses) there is a directed edge j → i. Thus the ith row of S identifies the edges coming into vertex i and their weights. This set of vertices are collectively the neighbors of i, and is denoted by Ni . The diagonal elements Sii are chosen such that each row sum equals 1. In particular, if a vertex i has no incoming edges, we choose Sii = 1. For the purposes of this work, we define the Laplacian by...

#### Locate the Document

#### Persistent Identifier

https://archives.pdx.edu/ds/psu/30107

#### Citation Details

Veerman, J.J.P., "Random Walks on Digraphs" (2017). *Mathematics and Statistics Faculty Publications and Presentations*. 263.

https://pdxscholar.library.pdx.edu/mth_fac/263

## Description

This is the author’s version of a work.Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document.