A measure of similarity between graph vertices
| dc.creator | Blondel, Vincent | |
| dc.creator | Gajardo, Anahi | |
| dc.creator | Heymans, Maureen | |
| dc.creator | Senellart, Pierre | |
| dc.creator | Van Dooren, Paul | |
| dc.date | 2004-07-28 | |
| dc.date.accessioned | 2026-07-07T06:38:04Z | |
| dc.date.available | 2026-07-07T06:38:04Z | |
| dc.description | We introduce a concept of similarity between vertices of directed graphs. Let G_A and G_B be two directed graphs. We define a similarity matrix whose (i, j)-th real entry expresses how similar vertex j (in G_A) is to vertex i (in G_B. The similarity matrix can be obtained as the limit of the normalized even iterates of a linear transformation. In the special case where G_A=G_B=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. | |
| dc.identifier | https://arxiv.org/abs/cs/0407061 | |
| dc.identifier | http://arxiv.org/abs/cs/0407061 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/100611 | |
| dc.subject | Information Retrieval | |
| dc.subject | Disordered Systems and Neural Networks | |
| dc.subject | Discrete Mathematics | |
| dc.subject | Data Analysis, Statistics and Probability | |
| dc.title | A measure of similarity between graph vertices | |
| dc.type | text |