A measure of similarity between graph vertices: Applications to synonym extraction and web searching

Blondel, VD; Gajardo A.; Heymans, M; Senellart, P; Van Dooren, P

Abstract

We introduce a concept of similarity between vertices of directed graphs. Let GA and GB be two directed graphs with, respectively, nA and nB vertices. We define an n B × nA similarity matrix S whose real entry sij expresses how similar vertex j (in GA) is to vertex i (in GB): we say that sij is their similarity score. The similarity matrix can be obtained as the limit of the normalized even iterates of Sk+1 = BSkA T + BTSkA, where A and B are adjacency matrices of the graphs and SO is a matrix whose entries are all equal to 1. In the special case where GA = G B = G, the matrix S is square and the score s ij is the similarity score between the vertices i and j of G. We point out that Kleinberg's "hub and authority" method to identify web-pages relevant to a given query can be viewed as a special case of our definition in the case where one of the graphs has two vertices and a unique directed edge between them. In analogy to Kleinberg, we show that our similarity scores are given by the components of a dominant eigenvector of a nonnegative matrix. Potential applications of our similarity concept are numerous. We illustrate an application for the automatic extraction of synonyms in a monolingual dictionary. © 2004 Society for Industrial and Applied Mathematics.

Más información

Título según WOS: A measure of similarity between graph vertices: Applications to synonym extraction and web searching
Título según SCOPUS: A measure of similarity between graph vertices: Applications to synonym extraction and web searching
Título de la Revista: SIAM REVIEW
Volumen: 46
Número: 4
Editorial: SIAM PUBLICATIONS
Fecha de publicación: 2004
Página de inicio: 647
Página final: 666
Idioma: English
URL: http://epubs.siam.org/doi/abs/10.1137/S0036144502415960
DOI:

10.1137/S0036144502415960

Notas: ISI, SCOPUS