# A survey of graph edit distance

@article{Gao2008ASO, title={A survey of graph edit distance}, author={Xinbo Gao and Bing Xiao and Dacheng Tao and Xuelong Li}, journal={Pattern Analysis and Applications}, year={2008}, volume={13}, pages={113-129} }

Inexact graph matching has been one of the significant research foci in the area of pattern analysis. As an important way to measure the similarity between pairwise graphs error-tolerantly, graph edit distance (GED) is the base of inexact graph matching. The research advance of GED is surveyed in order to provide a review of the existing literatures and offer some insights into the studies of GED. Since graphs may be attributed or non-attributed and the definition of costs for edit operations…

## 595 Citations

A Methodology to Generate Attributed Graphs with a Bounded Graph Edit Distance for Graph-Matching Testing

- Computer ScienceInt. J. Pattern Recognit. Artif. Intell.
- 2018

The methodology for generating pairs of attributed graphs with a lower and upper- bounded graph edit distance is presented and it is shown that with some restrictions, the methodology returns the optimal GED in a quadratic time and that it can be used to generate graph databases to test exact sub-graph isomorphism algorithms.

Detection of similar community in large network based on graph edit distance

- Computer Science2016 International Conference on Data Science and Engineering (ICDSE)
- 2016

First, a large network is taken and it is represented as an attributed graph then communities are discovered using GED, and the usefulness of the proposed method has been applied to Protein dataset and DBLP dataset.

A First Step Towards Exact Graph Edit Distance Using Bipartite Graph Matching

- Computer ScienceGbRPR
- 2015

This paper proposes an iterative version of one of the existing improvement strategies for graph edit distance computation that aims at further improving the overall distance quality while keeping the low computation time of the approximation framework.

Exploration of the Labelling Space Given Graph Edit Distance Costs

- Computer Science, MathematicsGbRPR
- 2011

New properties of the Graph Edit Distance are presented and it is shown that its minimization lead to a few different labellings and so, most of thelabellings in the labelling space cannot be obtained.

A comparative analysis of new graph distance measures and graph edit distance

- Computer ScienceInf. Sci.
- 2017

Sub-optimal Graph Matching by Node-to-Node Assignment Classification

- Computer ScienceGbRPR
- 2019

This work presents a new graph-matching algorithm that returns a graph correspondence without the explicit computation of the assignment problem thanks to a classification of the node-to-node assignment learned in a previous training stage.

Tolerant similarity search in graph database

- Computer Science2017 Computing Conference
- 2017

The proposed algorithm uses edge label & vertex label indexing and modifies inverted index based on substructures like star with labeled edges and edge substructure as substructure to maintain a global similarity order for subunits and graphs in case of star.

Comparing heuristics for graph edit distance computation

- Computer Science, BusinessThe VLDB Journal
- 2019

This paper empirically evaluate all compared heuristics within an integrated implementation of the graph edit distance and provides a systematic overview of the most importantHeuristics.

Iterative Bipartite Graph Edit Distance Approximation

- Computer Science2014 11th IAPR International Workshop on Document Analysis Systems
- 2014

A generalized version of the existing approximation framework using an iterative bipartite procedure is introduced and it is shown that the extension substantially improves the accuracy of the approximations while the run time is increased only linearly with the number of additional iterations.

An Efficient Probabilistic Approach for Graph Similarity Search

- Computer Science2018 IEEE 34th International Conference on Data Engineering (ICDE)
- 2018

This paper proposes a novel probabilistic approach to efficiently estimate GED, and introduces a novel graph similarity measure by comparing branches between graphs, i.e., Graph Branch Distance (GBD), which can be efficiently calculated in polynomial time.

## References

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This paper proposes a novel convolution graph kernel, which differs from other graph kernels mainly in that it is closely related to error-tolerant graph edit distance and can therefore be applied to attributed graphs of various kinds.

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A system of self-organizing maps (SOMs) that represent the distance measuring spaces of node and edge labels are proposed that adapts the edit costs in such a way that the similarity of graphs from the same class is increased, whereas the similarity from different classes decreases.

A probabilistic approach to learning costs for graph edit distance

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This work proposes a cost inference method that is based on a distribution estimation of edit operations that employs an expectation maximization algorithm to learn mixture densities from a labeled sample of graphs and derive edit costs that are subsequently applied in the context of a graph edit distance computation framework.

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The aim is to convert graphs to string sequences so that standard string edit distance techniques can be used, and uses graph spectral seriation method to convert the adjacency matrix into a string or sequence order.

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A binary linear programming formulation of the graph edit distance

- Computer ScienceIEEE Transactions on Pattern Analysis and Machine Intelligence
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A binary linear programming formulation of the graph edit distance for unweighted, undirected graphs with vertex attributes is derived and applied to a graph recognition problem, and the new metric is shown to perform quite well in comparison to existing metrics when applications to a database of chemical graphs.

Edit Distance Based Kernel Functions for Attributed Graph Matching

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It is shown in experiments on real-world data that the kernel approach may result in a significant improvement of the graph matching and classification performance using support vector machines and kernel principal component analysis.