# A LexDFS-Based Approach on Finding Compact Communities

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## Abstract

This article presents an efficient hierarchical clustering algorithm based on a graph traversal algorithm called LexDFS. This traversal algorithm has the property of going through the clustered parts of the graph in a small number of iterations, making them recognisable. The time complexity of our method is in *O*(*n* × log(*n*)). It is simple to implement and a thorough study shows that it outputs clusterings that are closer to some ground-truths than its competitors. Experiments are also carried out to analyse the behaviour of the algorithm during execution on sample graphs. This article also features a quality function called *compactness*, which measures how efficient is the cluster for internal communications. We prove that this quality function features interesting theoretical properties.

## Keywords

Community detection Compactness LexDFS## Notes

### Acknowledgements

The authors thank Loïck Lhote for his help with the proof of continuity.

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