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Additional resources for Graph classification and clustering based on vector space embedding
In the former case, for a matching to be successful, it is required that a strict correspondence is found between the two graphs being matched, or at least among their subparts. In the latter approach this requirement is substantially relaxed, since also matchings between completely non-identical graphs are possible. That is, inexact matching algorithms are endowed with a certain tolerance to errors and noise, enabling them to detect similarities in a more general way than the exact matching approach.
Let g1 = (V1 , E1 , µ1 , ν1 ) and g2 = (V2 , E2 , µ2 , ν2 ) be graphs. A common supergraph December 28, 2009 26 9:59 Classification and Clustering clustering Graph Classification and Clustering Based on Vector Space Embedding of g1 and g2 , CS(g1 , g2 ), is a graph g = (V, E, µ, ν) such that there exist subgraph isomorphisms from g1 to g and from g2 to g. We call g a minimum common supergraph of g1 and g2 , M CS(g1 , g2 ), if there exists no other common supergraph of g1 and g2 that has less nodes than g.
In practice, however, a few weak conditions on the cost function c are sufficient so that December 28, 2009 40 9:59 Classification and Clustering clustering Graph Classification and Clustering Based on Vector Space Embedding only a finite number of edit paths have to be evaluated to find the minimum cost edit path among all valid paths between two given graphs. e. c(e) ≥ 0 , for all node and edge edit operations e. 1) We refer to this condition as non-negativity. Since the cost function assigns a penalty cost to a certain edit operation, this condition is certainly reasonable.