Graph distances using graph union

Wallis, W. D.; Shoubridge, Peter; Kraetz, M.; Ray, Dipojjwal

doi:10.1016/s0167-8655(01)00022-8

Cited by 122 publications

(69 citation statements)

References 13 publications

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“…Several models have been proposed [23], [24], [25] to measure the similarity (or distance) between two graphs. Hereafter, we present the most widely accepted measures to determine similarities between graphs 1 .…”

Section: Graph Similarity Measures: Some Semantic Propertiesmentioning

confidence: 99%

“…Graph union(Gu)-based distance measure, introduced by Wallis et al [25], is based on the idea of graph union. Graph union (rather than the larger of two graphs) is used to model the size of the problem.…”

Section: Gu-based Distancementioning

confidence: 99%

“…The use of graph union [25] is motivated by the fact that changes in the size of the smallest graph that keep ( 1 , 2 ) constant are not taken into account in ( 1 , 2 ) whereas the measure ( 1 , 2 ) does take this variation into account. The graph distance measure derived from can be written as:…”

Section: Gu-based Distancementioning

confidence: 99%

See 2 more Smart Citations

A similarity skyline approach for handling graph queries - A preliminary report

Abbaci

Hadjali

Liétard

et al. 2011

2011 IEEE 27th International Conference on Data Engineering Workshops

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Abstract-One of the fundamental problems in graph databases is similarity search for graphs of interest. Existing approaches dealing with this problem rely on a single similarity measure between graph structures. In this paper, we suggest an alternative approach allowing for searching similar graphs to a graph query where similarity between graphs is rather modeled by a vector of scalars than a unique scalar. To this end, we introduce the notion of similarity skyline of a graph query defined by the subset of graphs of the target database that are the most similar to the query in a Pareto sense. The idea is to achieve a d-dimensional comparison between graphs in terms of local distance (or similarity) measures and to retrieve those graphs that are maximally similar in the sense of the Pareto dominance relation. A diversity-based method for refining the retrieval result is proposed as well.

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Section: Graph Similarity Measures: Some Semantic Propertiesmentioning

confidence: 99%

Section: Gu-based Distancementioning

confidence: 99%

See 1 more Smart Citation

A similarity skyline approach for handling graph queries - A preliminary report

Abbaci

Hadjali

Liétard

et al. 2011

2011 IEEE 27th International Conference on Data Engineering Workshops

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show abstract

“…It is interesting to note that the Wallis et al [21] formula (C1) is mathematically equivalent to the Tanimoto [3] formula (F1), and the Johnson b [22] measure (C5) is equivalent to the cosine [3] measure (F2) squared. In addition, C4, the normalized variation of another measure attributed to…”

Section: Consists Of a Set Of Vertices V(g) And A Set Of Edges E(g)mentioning

confidence: 99%

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Raymond

Willett

2002

Journal of Computer-Aided Molecular Design

101

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This paper reports an evaluation of both graph-based and fingerprint-based measures of structural similarity, when used for virtual screening of sets of 2D molecules drawn from the MDDR and ID Alert databases. The graph-based measures employ a new maximum common edge subgraph isomorphism algorithm, called RASCAL, with several similarity coefficients described previously for quantifying the similarity between pairs of graphs. The effectiveness of these graph-based searches is compared with that resulting from similarity searches using BCI, Daylight and Unity 2D fingerprints. Our results suggest that graph-based approaches provide an effective complement to existing fingerprint-based approaches to virtual screening.

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“…As a result, various graph distance measures have been proposed in the literatures [1,5,6,19,24,26,27].…”

Section: Introductionmentioning

confidence: 99%

Structure-based graph distance measures of high degree of precision

Dong

Xiong

et al. 2008

Pattern Recognition

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In recent years, evaluating graph distance has become more and more important in a variety of real applications and many graph distance measures have been proposed. Among all of those measures, structure-based graph distance has become the research focus due to its independence of the definition of cost function. However, the existing structure-based graph distance measures have low degree of precision because only node and edge information of graphs are employed in these graphs metrics. To improve the precision of graph distance measure, we define a substructure abundance vector (SAV) to capture more substructure information of a graph. Furthermore, based on the SAV, we propose unified graph distance measures which are generalization of the existing structurebased graph distance measures. In general, the unified graph distance measures can evaluate graph distance in much finer grain. We also show that unified graph distance measures based on occurrence mapping and some of their variants are metrics. Finally, we apply the unified graph distance metric and its variants to the population evolution analysis and construct distance graphs of marker networks in three populations, which reflect the single nucleotide polymorphism (SNP) linkage disequilibrium (LD) differences among these populations.

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Graph distances using graph union

Cited by 122 publications

References 13 publications

A similarity skyline approach for handling graph queries - A preliminary report

A similarity skyline approach for handling graph queries - A preliminary report

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Structure-based graph distance measures of high degree of precision

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