@article{Blondel2004a,
abstract = {We introduce a concept of similarity between vertices of directed graphs. Let GA and GB be two directed graphs. We define a similarity matrix whose (i, j)-th real entry expresses how similar vertex j (in GA) is to vertex i (in GB. The similarity matrix can be obtained as the limit of the normalized even iterates of a linear transformation. In the special case where GA=GB=G, the matrix is square and the (i, j)-th entry 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 non-negative matrix. Potential applications of our similarity concept are numerous. We illustrate an application for the automatic extraction of synonyms in a monolingual dictionary.},
annote = {
        From Duplicate 1 ( 
        
        
          A measure of similarity between graph vertices
        
        
         - Blondel, Vincent; Gajardo, Anahi; Heymans, Maureen; Senellart, Pierre; Van Dooren, Paul )

        
        

        

        

      },
author = {Blondel, Vincent D. and Gajardo, Anahi and Heymans, Maureen and Senellart, Pierre and {Van Dooren}, Paul},
journal = {Technology},
keywords = {SML-LIB-BIBLIO,lang:ENG},
mendeley-tags = {SML-LIB-BIBLIO,lang:ENG},
pages = {647--666},
publisher = {JSTOR},
title = {{A measure of similarity between graph vertices}},
url = {http://arxiv.org/abs/cs/0407061},
year = {2004}
}