A Unified Framework for Affine Local Graph Similarity

In this work, we review and classify several similarity measures on undirected graphs. We show that these measures can be rewritten in terms of fixed points of a scaled affine transformation. Finally, we propose a novel definition that avoids undesirable degeneracy of the similarity matrix.

[1]  Yizhou Sun,et al.  P-Rank: a comprehensive structural similarity measure over information networks , 2009, CIKM.

[2]  Linyuan Lü,et al.  Predicting missing links via local information , 2009, 0901.0553.

[3]  Loet Leydesdorff,et al.  On the normalization and visualization of author co-citation data: Salton's Cosine versus the Jaccard index , 2009, J. Assoc. Inf. Sci. Technol..

[4]  P. Holme,et al.  Role-similarity based functional prediction in networked systems: application to the yeast proteome , 2005, Journal of The Royal Society Interface.

[5]  Paul Van Dooren,et al.  A MEASURE OF SIMILARITY BETWEEN GRAPH VERTICES . WITH APPLICATIONS TO SYNONYM EXTRACTION AND WEB SEARCHING , 2002 .

[6]  Ambuj K. Singh,et al.  Deriving phylogenetic trees from the similarity analysis of metabolic pathways , 2003, ISMB.

[7]  Lada A. Adamic,et al.  Friends and neighbors on the Web , 2003, Soc. Networks.

[8]  S. Borgatti,et al.  Defining and measuring trophic role similarity in food webs using regular equivalence. , 2003, Journal of theoretical biology.

[9]  A. Barabasi,et al.  Hierarchical Organization of Modularity in Metabolic Networks , 2002, Science.

[10]  Jennifer Widom,et al.  SimRank: a measure of structural-context similarity , 2002, KDD.

[11]  Erhard Rahm,et al.  Similarity flooding: a versatile graph matching algorithm and its application to schema matching , 2002, Proceedings 18th International Conference on Data Engineering.

[12]  M. KleinbergJon.  Authoritative sources in a hyperlinked environment , 1999 .

[13]  Stanley Wasserman,et al.  Social Network Analysis: Methods and Applications , 1994, Structural analysis in the social sciences.

[14]  Alexandru T. Balaban,et al.  Applications of graph theory in chemistry , 1985, J. Chem. Inf. Comput. Sci..

[15]  Michael McGill,et al.  Introduction to Modern Information Retrieval , 1983 .

[16]  K. Reitz,et al.  Graph and Semigroup Homomorphisms on Networks of Relations , 1983 .

[17]  D. A. Waller,et al.  Kronecker Products and Local Joins of Graphs , 1977, Canadian Journal of Mathematics.

[18]  Eilif Dahl.  Some Measures of Uniformity in Vegetation Analysis , 1960 .

[19]  T. Sørensen,et al.  A method of establishing group of equal amplitude in plant sociobiology based on similarity of species content and its application to analyses of the vegetation on Danish commons , 1948 .

[20]  P. Jaccard,et al.  Etude comparative de la distribution florale dans une portion des Alpes et des Jura , 1901 .