Graph labelings obtainable by random walks

Random Walks and Graph Homomorphisms

Graph homomorphisms through random walks

In this paper we introduce some general necessary conditions for the existence of graph homomorphisms, which hold in both directed and undirected cases. Our method is a combination of Diaconis and Saloff– Coste comparison technique for Markov chains and a generalization of Haemers interlacing theorem. As some applications, we obtain a necessary condition for the spanning subgraph problem, which...

Lecture 12 : Random Walks and Graph Centrality

We now present a different type of connection between graphs and eigenvalues. In several applications, we wish to find influential vertices in a graph. For instance, suppose we model Twitter as a directed graph where there is an edge from user i to user j if i follows j. Then how can we measure importance of a user in the graph? One way of measuring it is look at the in-degree of a user, or the...

Lexical Semantic Relatedness with Random Graph Walks

Many systems for tasks such as question answering, multi-document summarization, and information retrieval need robust numerical measures of lexical relatedness. Standard thesaurus-based measures of word pair similarity are based on only a single path between those words in the thesaurus graph. By contrast, we propose a new model of lexical semantic relatedness that incorporates information fro...

Algorithmic aspects of graph-indexed random walks

Graph-indexed random walks (or equivalently M -Lipschitz mappings of graphs) are a generalization of standard random walk on Z. For M ∈ N, an M-Lipschitz mapping of a connected rooted graph G = (V,E) is a mapping f : V → Z such that root is mapped to zero and for every edge (u, v) ∈ E we have |f(u) − f(v)| ≤ M . We study two natural problems regarding graph-indexed random walks. 1. Computing th...