Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-10T16:10:10.306Z Has data issue: false hasContentIssue false
  • English
  • Français

Superbubbles as an empirical characteristic of directed networks

Published online by Cambridge University Press:  01 September 2020

Fabian Gärtner ,
Felix Kühnl Open the ORCID record for Felix Kühnl [Opens in a new window] ,
Carsten R. Seemann Open the ORCID record for Carsten R. Seemann [Opens in a new window] ,
Christian Höner Zu Siederdissen Open the ORCID record for Christian Höner Zu Siederdissen [Opens in a new window] ,
Peter F. Stadler Open the ORCID record for Peter F. Stadler [Opens in a new window]  and
The Students of the Graphs and Networks Computer Lab 2018/19
Fabian Gärtner
Affiliation:
Competence Center for Scalable Data Services and Solutions Dresden/Leipzig (scaDS), Universität Leipzig, Augustusplatz 12, D-04107 Leipzig, Germany (e-mail: fabian@bioinf.uni-leipzig.de) Bioinformatics Group, Department of Computer Science, Universität Leipzig, Härtelstraße 16-18, D-04107 Leipzig, Germany (e-mails: carsten@bioinf.uni-leipzig.de, felix@bioinf.uni-leipzig.de, choener@bioinf.uni-leipzig.de)
Felix Kühnl
Affiliation:
Bioinformatics Group, Department of Computer Science, Universität Leipzig, Härtelstraße 16-18, D-04107 Leipzig, Germany (e-mails: carsten@bioinf.uni-leipzig.de, felix@bioinf.uni-leipzig.de, choener@bioinf.uni-leipzig.de) Interdisciplinary Center for Bioinformatics, Universität Leipzig, Härtelstraße 16-18, D-04107 Leipzig, Germany
Carsten R. Seemann
Affiliation:
Bioinformatics Group, Department of Computer Science, Universität Leipzig, Härtelstraße 16-18, D-04107 Leipzig, Germany (e-mails: carsten@bioinf.uni-leipzig.de, felix@bioinf.uni-leipzig.de, choener@bioinf.uni-leipzig.de) Interdisciplinary Center for Bioinformatics, Universität Leipzig, Härtelstraße 16-18, D-04107 Leipzig, Germany Max Planck Institute for Mathematics in the Sciences, Inselstraße 22, D-04103 Leipzig, Germany
Christian Höner Zu Siederdissen
Affiliation:
Bioinformatics Group, Department of Computer Science, Universität Leipzig, Härtelstraße 16-18, D-04107 Leipzig, Germany (e-mails: carsten@bioinf.uni-leipzig.de, felix@bioinf.uni-leipzig.de, choener@bioinf.uni-leipzig.de) Interdisciplinary Center for Bioinformatics, Universität Leipzig, Härtelstraße 16-18, D-04107 Leipzig, Germany
Peter F. Stadler*
Affiliation:
Competence Center for Scalable Data Services and Solutions Dresden/Leipzig (scaDS), Universität Leipzig, Augustusplatz 12, D-04107 Leipzig, Germany (e-mail: fabian@bioinf.uni-leipzig.de) Bioinformatics Group, Department of Computer Science, Universität Leipzig, Härtelstraße 16-18, D-04107 Leipzig, Germany (e-mails: carsten@bioinf.uni-leipzig.de, felix@bioinf.uni-leipzig.de, choener@bioinf.uni-leipzig.de) Interdisciplinary Center for Bioinformatics, Universität Leipzig, Härtelstraße 16-18, D-04107 Leipzig, Germany Max Planck Institute for Mathematics in the Sciences, Inselstraße 22, D-04103 Leipzig, Germany German Centre for Integrative Biodiversity Research (iDiv) Halle-Jena-Leipzig, Universität Leipzig, Härtelstraße 16-18, D-04107 Leipzig, Germany Leipzig Research Center for Civilization Diseases, Universität Leipzig, Härtelstraße 16-18, D-04107 Leipzig, Germany Institute for Theoretical Chemistry, University of Vienna, Währingerstraße17, A-1090 Wien, Austria Facultad de Ciencias, Universidad National de Colombia, Sede Bogotá, Colombia Santa Fe Institute, 1399 Hyde Park Rd., Santa Fe, NM87501, USA
The Students of the Graphs and Networks Computer Lab 2018/19
Affiliation:
Bioinformatics Group, Department of Computer Science, Universität Leipzig, Härtelstraße 16-18, D-04107 Leipzig, Germany (e-mails: carsten@bioinf.uni-leipzig.de, felix@bioinf.uni-leipzig.de, choener@bioinf.uni-leipzig.de)
*
*Corresponding author. Email: studla@bioinf.uni-leipzig.de
Get access Rights & Permissions [Opens in a new window]

Abstract

Superbubbles are acyclic induced subgraphs of a digraph with single entrance and exit that naturally arise in the context of genome assembly and the analysis of genome alignments in computational biology. These structures can be computed in linear time and are confined to non-symmetric digraphs. We demonstrate empirically that graph parameters derived from superbubbles provide a convenient means of distinguishing different classes of real-world graphical models, while being largely unrelated to simple, commonly used parameters.

Keywords

digraphgraph descriptorbubbleslinear time algorithm
Type
Research Article
Information
Network Science , Volume 9 , Issue 1 , March 2021 , pp. 49 - 58
Copyright
© The Author(s), 2020. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

Action Editor: Ulrik Brandes

References

Alon, N., Yuster, R., & Zwick, U. (1997). Finding and counting given length cycles. Algorithmica, 17, 209–223.CrossRefGoogle Scholar
Anderson, W. N., & Morley, T. D. (1985). Eigenvalues of the Laplacian of a graph. Linear and Multilinear Algebra, 18, 141–145.CrossRefGoogle Scholar
Bang-Jensen, J., & Gutin, G. Z. (2009). Digraphs: Theory, algorithms and applications. London, UK: Springer-Verlag.CrossRefGoogle Scholar
Barabási, A.-L. (2016). Network science. Cambridge, UK: Cambridge Univ. Press.Google Scholar
Barabási, A.-L., & Albert, R. (1999). Emergence of scaling in random networks. Science, 286, 509–512.CrossRefGoogle ScholarPubMed
Bollobás, B., Borgs, C., Chayes, J., & Riordan, O. (2003). Directed scale-free graphs. In Proceedings of the 14th annual acm-siam symposium on discrete algorithms (soda) (pp. 132–139). Philadelphia, PA: Society for Industrial and Applied Mathematics.Google Scholar
Brandes, U. (2001). A faster algorithm for betweenness centrality. The Journal of Mathematical Sociology, 25, 163–177.CrossRefGoogle Scholar
Brankovic, L., Iliopoulos, C. S., Kundu, R., Mohamed, M., Pissis, S. P., & Vayani, F. (2016). Linear-time superbubble identification algorithm for genome assembly. Theoretical Computer Science, 609, 374–383.CrossRefGoogle Scholar
Capotă, M., Hegeman, T., Iosup, A., Prat-Pérez, A., Erling, O., & Boncz, P. (2015). Graphalytics: A big data benchmark for graph-processing platforms. In Grades 2015 (p. 7). New York: ACM.Google Scholar
Devillers, J., & Balaban, A. T. (Eds.) (2000). Topological indices and related descriptors in QSAR and QSPAR. Boca Raton, FL: CRC Press.CrossRefGoogle Scholar
Drillon, G., & Fischer, G. (2011). Comparative study on synteny between yeasts and vertebrates. Comptes Rendus Biologies, 334, 629–638.CrossRefGoogle ScholarPubMed
Erdős, P., & Rényi, A. (1959). On random graphs. Publicationes Mathematicae Debrecen, 6, 290–297.Google Scholar
Foster, J. G., Foster, D. V., Grassberger, P., & Paczuski, M. (2010). Edge direction and the structure of networks. Proceedings of the National Academy of Sciences of the United States of America, 107, 10815–10820.CrossRefGoogle Scholar
Gärtner, F. (2020). Comparative genomics in distant taxa. Ph.D. thesis, Leipzig University.Google Scholar
Gärtner, F., Höner zu Siederdissen, C., Müller, L., & Stadler, P. F. (2018a). Coordinate systems for supergenomes. Algorithms for Molecular Biology, 13, 15.CrossRefGoogle ScholarPubMed
Gärtner, F., Müller, L., & Stadler, P. F. (2018b). Superbubbles revisited. Algorithms for Molecular Biology, 13, 16.CrossRefGoogle ScholarPubMed
Gärtner, F., & Stadler, P. F. (2019). Direct superbubble detection. Algorithms, 12, 81.CrossRefGoogle Scholar
Hage, P., & Harary, F. (1995). Eccentricity and centrality in networks. Social Networks, 17, 57–63.CrossRefGoogle Scholar
Herbig, A, Jäger, G., Battke, F., & Nieselt, K. (2012). GenomeRing: Alignment visualization based on SuperGenome coordinates. Bioinformatics, 28, i7–i15.CrossRefGoogle ScholarPubMed
Leskovec, J., & Sosič, R. (2016). SNAP: A general-purpose network analysis and graph-mining library. ACM Transactions on Intelligent Systems and Technology, 8, 1.CrossRefGoogle ScholarPubMed
Li, L., Alderson, D., Doyle, J. C., & Willinger, W. (2005). Towards a theory of scale-free graphs: Definition, properties, and implications. Internet Mathematics, 2, 431–523.CrossRefGoogle Scholar
Metcalf, L., & Casey, W. (2016). Cybersecurity and applied mathematics. Syngress.Google Scholar
Mubayi, D., Will, T. G., & West, D. B. (2001). Realizing degree imbalances in directed graphs. Discrete Mathematics, 239, 147–153.CrossRefGoogle Scholar
Murphy, R. C., Wheeler, K. B., Barrett, B. W., & Ang, J. A. (2010). Introducing the Graph 500. Tech. rept. Cray Users Group (CUG).Google Scholar
Newman, M. E. J. (2003). Mixing patterns in networks. Physical Review E, 67, 026126.CrossRefGoogle ScholarPubMed
Onodera, T., Sadakane, K., & Shibuya, T. (2013). Detecting superbubbles in assembly graphs. In Darling, A., & Stoye, J. (Eds.), International workshop on algorithms in bioinformatics (pp. 338–348), vol. 8126. Berlin, Heidelberg: Springer Verlag.CrossRefGoogle Scholar
Paten, B., Eizenga, J. M., Rosen, Y. M., Novak, A. M., Garrison, E., & Hickey, G. (2018). Superbubbles, ultrabubbles, and cacti. Journal of Computational Biology, 25, 649–663.CrossRefGoogle ScholarPubMed
Sabidussi, G. (1966). The centrality index of a graph. Psychometrika, 31, 581–603.CrossRefGoogle Scholar
Sammeth, M. (2009). Complete alternative splicing events are bubbles in splicing graphs. Journal of Computational Biology, 16, 1117–1140.CrossRefGoogle ScholarPubMed
Shimbel, A. (1953). Structural parameters of communication networks. Bulletin of Mathematical Biology, 15, 501–507.Google Scholar
Sung, W.-K., Sadakane, K., Shibuya, T., Belorkar, A., & Pyrogova, I. (2015). An O(m log m)-time algorithm for detecting superbubbles. IEEE/ACM Transactions on Computational Biology and Bioinformatics, 12, 770–777.CrossRefGoogle Scholar
Tarjan, R. (1972). Depth-first search and linear graph algorithms. SIAM Journal on Computing, 1, 146–160.CrossRefGoogle Scholar
Watts, D., & Strogatz, S. H. (1998). Collective dynamics of small-world networks. Nature, 393, 440–442.CrossRefGoogle Scholar
Ye, C., Wilson, R. C., Comin, C. H., da F. Costa, L., & Hancock, E. R. (2013). Entropy and heterogeneity measures for directed graphs. In Similarity-based pattern recognition (pp. 219–234). Berlin Heidelberg: Springer.CrossRefGoogle Scholar
Supplementary material: PDF

Gärtner et al. Supplementary Materials

Gärtner et al. Supplementary Materials

Download Gärtner et al. Supplementary Materials(PDF)
PDF 142.3 KB