Graph automorphisms for compression

Uroš Čibej 1  and Jurij Mihelič 2
  • 1 University of Ljubljana, Faculty of Computer and Information Science, Večna pot 113, 1000, Ljubljana, Slovenia
  • 2 University of Ljubljana, Faculty of Computer and Information Science, Večna pot 113, 1000, Ljubljana, Slovenia


Detecting automorphisms is a natural way to identify redundant information presented in structured data. When such redundancies are detected they can be used for data compression. In this paper we explore two different classes of graphs to capture this intuitive property of automorphisms. Symmetry-compressible graphs are the first class which introduces the basic concepts but use only global symmetries for the compression. In order for this concept to be more practical, we need to use local symmetries. Thus, we extend the basic graph class with Near Symmetry compressible graphs. Furthermore, we develop two algorithms that can be used to compress practical instances and empirically evaluate them on a set of realistic graphs.

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  • [1] Sandra Álvarez, Nieves R Brisaboa, Susana Ladra, and Óscar Pedreira. A compact representation of graph databases. In Proceedings of the Eighth Workshop on Mining and Learning with Graphs, pages 18–25, 2010.

  • [2] Vo Ngoc Anh and Alistair Moffat. Local modeling for webgraph compression. In 2010 Data Compression Conference, pages 519–519. IEEE, 2010.

  • [3] Maciej Besta and Torsten Hoefler. Survey and taxonomy of lossless graph compression and space-efficient graph representations. arXiv preprint arXiv:1806.01799, 2018.

  • [4] Dongbo Bu, Yi Zhao, Lun Cai, Hong Xue, Xiaopeng Zhu, Hongchao Lu, Jingfen Zhang, Shiwei Sun, Lunjiang Ling, Nan Zhang, et al. Topological structure analysis of the protein–protein interaction network in budding yeast. Nucleic acids research, 31(9):2443–2450, 2003.

  • [5] Uroš Čibej and Jurij Mihelič. Improvements to Ullmann’s algorithm for the subgraph isomorphism problem. International Journal of Pattern Recognition and Artificial Intelligence, 29(07), 2015.

  • [6] Luigi P Cordella, Pasquale Foggia, Carlo Sansone, and Mario Vento. A (sub) graph isomorphism algorithm for matching large graphs. IEEE transactions on pattern analysis and machine intelligence, 26(10):1367–1372, 2004.

  • [7] Olivier Cure, Hubert Naacke, Tendry Randriamalala, and Bernd Amann. Litemat: a scalable, cost-efficient inference encoding scheme for large rdf graphs. In 2015 IEEE International Conference on Big Data (Big Data), pages 1823–1830. IEEE, 2015.

  • [8] Arash Farzan and J Ian Munro. Succinct encoding of arbitrary graphs. Theoretical Computer Science, 513:38–52, 2013.

  • [9] Pablo M Gleiser and Leon Danon. Community structure in jazz. Advances in complex systems, 6(04):565–573, 2003.

  • [10] Camille Jordan. Sur les assemblages de lignes. Journal für die reine und angewandte Mathematik, 1869(70):185–190, 1869.

  • [11] Jure Leskovec and Julian J Mcauley. Learning to discover social circles in ego networks. In Advances in neural information processing systems, pages 539–547, 2012.

  • [12] Faming Li, Zhaonian Zou, Jianzhong Li, and Yingshu Li. Graph compression with stars. In Pacific-Asia Conference on Knowledge Discovery and Data Mining, pages 449–461. Springer, 2019.

  • [13] Sebastian Maneth and Fabian Peternek. Grammar-based graph compression. Information Systems, 76:19–45, 2018.

  • [14] Francesco Pelosin. Graph compression using the regularity method. arXiv preprint arXiv:1810.07275, 2018.

  • [15] David Reinsel, John Gantz, and John Rydning. Data age 2025: the digitization of the world from edge to core. Seagate,, 2018.

  • [16] Ian Robinson, Jim Webber, and Emil Eifrem. Graph databases: new opportunities for connected data. O’Reilly Media, Inc., 2015.

  • [17] Ryan A Rossi and Rong Zhou. Graphzip: a clique-based sparse graph compression method. Journal of Big Data, 5(1):10, 2018.

  • [18] Duncan J Watts and Steven H Strogatz. Collective dynamics of ‘small-world’networks. Nature, 393(6684):440–442, 1998.

  • [19] Wayne W Zachary. An information flow model for conflict and fission in small groups. Journal of anthropological research, pages 452–473, 1977.


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