Document Open Access Logo

A Family of Centrality Measures for Graph Data Based on Subgraphs

Authors Cristian Riveros, Jorge Salas



PDF
Thumbnail PDF

File

LIPIcs.ICDT.2020.23.pdf
  • Filesize: 0.5 MB
  • 18 pages

Document Identifiers

Author Details

Cristian Riveros
  • Pontificia Universidad Católica de Chile, Santiago, Chile
  • Millennium Institute for Foundational Research on Data, Santiago, Chile
Jorge Salas
  • Pontificia Universidad Católica de Chile, Santiago, Chile
  • Millennium Institute for Foundational Research on Data, Santiago, Chile

Cite AsGet BibTex

Cristian Riveros and Jorge Salas. A Family of Centrality Measures for Graph Data Based on Subgraphs. In 23rd International Conference on Database Theory (ICDT 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 155, pp. 23:1-23:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)
https://doi.org/10.4230/LIPIcs.ICDT.2020.23

Abstract

We present the theoretical foundations of a new approach in centrality measures for graph data. The main principle of our approach is very simple: the more relevant subgraphs around a vertex, the more central it is in the network. We formalize the notion of "relevant subgraphs" by choosing a family of subgraphs that, give a graph G and a vertex v in G, it assigns a subset of connected subgraphs of G that contains v. Any of such families defines a measure of centrality by counting the number of subgraphs assigned to the vertex, i.e., a vertex will be more important for the network if it belongs to more subgraphs in the family. We show many examples of this approach and, in particular, we propose the all-subgraphs centrality, a centrality measure that takes every subgraph into account. We study fundamental properties over families of subgraphs that guarantee desirable properties over the corresponding centrality measure. Interestingly, all-subgraphs centrality satisfies all these properties, showing its robustness as a notion for centrality. Finally, we study the computational complexity of counting certain families of subgraphs and show a polynomial time algorithm to compute the all-subgraphs centrality for graphs with bounded tree width.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph theory
  • Information systems → Graph-based database models
Keywords
  • Graph data
  • graph centrality
  • centrality measures

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads

References

  1. Renzo Angles, Marcelo Arenas, Pablo Barceló, Aidan Hogan, Juan L. Reutter, and Domagoj Vrgoc. Foundations of Modern Query Languages for Graph Databases. ACM Comput. Surv., 50(5):68:1-68:40, 2017. Google Scholar
  2. Sanjeev Arora and Boaz Barak. Computational complexity: a modern approach. Cambridge University Press, 2009. Google Scholar
  3. Sambaran Bandyopadhyay, Ramasuri Narayanam, and M Narasimha Murty. A Generic Axiomatic Characterization for Measuring Influence in Social Networks. In 2018 24th International Conference on Pattern Recognition (ICPR), pages 2606-2611. IEEE, 2018. Google Scholar
  4. Alex Bavelas. Communication patterns in task-oriented groups. The Journal of the Acoustical Society of America, 22(6):725-730, 1950. Google Scholar
  5. Paolo Boldi, Alessandro Luongo, and Sebastiano Vigna. Rank monotonicity in centrality measures. Network Science, 5(4):529-550, 2017. Google Scholar
  6. Paolo Boldi and Sebastiano Vigna. Axioms for centrality. Internet Mathematics, 10(3-4):222-262, 2014. Google Scholar
  7. Stephen P Borgatti and Martin G Everett. A graph-theoretic perspective on centrality. Social networks, 28(4):466-484, 2006. Google Scholar
  8. Ulrik Brandes. Network analysis: methodological foundations, volume 3418. Springer Science & Business Media, 2005. Google Scholar
  9. Sergey Brin and Lawrence Page. The anatomy of a large-scale hypertextual web search engine. Computer networks and ISDN systems, 30(1-7):107-117, 1998. Google Scholar
  10. Carlos Buil-Aranda, Martın Ugarte, Marcelo Arenas, and Michel Dumontier. A preliminary investigation into SPARQL query complexity and federation in Bio2RDF. In Alberto Mendelzon International Workshop on Foundations of Data Management, page 196, 2015. Google Scholar
  11. Steve Chien, Cynthia Dwork, Ravi Kumar, Daniel R Simon, and D Sivakumar. Link evolution: Analysis and algorithms. Internet mathematics, 1(3):277-304, 2004. Google Scholar
  12. Thomas M Cover and Joy A Thomas. Elements of information theory. John Wiley & Sons, 2012. Google Scholar
  13. Ernesto Estrada and Juan A Rodriguez-Velazquez. Subgraph centrality in complex networks. Physical Review E, 71(5):056103, 2005. Google Scholar
  14. Mohammad Reza Faghani and Uyen Trang Nguyen. A study of XSS worm propagation and detection mechanisms in online social networks. IEEE transactions on information forensics and security, 8(11):1815-1826, 2013. Google Scholar
  15. Linton C Freeman. A set of measures of centrality based on betweenness. Sociometry, pages 35-41, 1977. Google Scholar
  16. Linton C Freeman. Centrality in social networks conceptual clarification. Social networks, 1(3):215-239, 1978. Google Scholar
  17. Manuj Garg. Axiomatic foundations of centrality in networks. Available at SSRN 1372441, 2009. Google Scholar
  18. Georg Gottlob, Gianluigi Greco, Nicola Leone, and Francesco Scarcello. Hypertree Decompositions: Questions and Answers. In Proceedings of the 35th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems, PODS 2016, San Francisco, CA, USA, June 26 - July 01, 2016, pages 57-74, 2016. Google Scholar
  19. Hawoong Jeong, Sean P Mason, A-L Barabási, and Zoltan N Oltvai. Lethality and centrality in protein networks. Nature, 411(6833):41, 2001. Google Scholar
  20. Leo Katz. A new status index derived from sociometric analysis. Psychometrika, 18(1):39-43, 1953. Google Scholar
  21. Harold J Leavitt. Some effects of certain communication patterns on group performance. The Journal of Abnormal and Social Psychology, 46(1):38, 1951. Google Scholar
  22. Johannes Lorey and Felix Naumann. Detecting SPARQL query templates for data prefetching. In Extended Semantic Web Conference, pages 124-139. Springer, 2013. Google Scholar
  23. Silviu Maniu, Pierre Senellart, and Suraj Jog. An Experimental Study of the Treewidth of Real-World Graph Data. In 22nd International Conference on Database Theory, ICDT 2019, March 26-28, 2019, Lisbon, Portugal, pages 12:1-12:18, 2019. Google Scholar
  24. Gonzalo Navarro. Compact data structures: A practical approach. Cambridge University Press, 2016. Google Scholar
  25. Mark Newman. Networks: an introduction. Oxford university press, 2010. Google Scholar
  26. Neil Robertson and Paul D Seymour. Graph minors. III. Planar tree-width. Journal of Combinatorial Theory, Series B, 36(1):49-64, 1984. Google Scholar
  27. Gert Sabidussi. The centrality index of a graph. Psychometrika, 31(4):581-603, 1966. Google Scholar
  28. Oskar Skibski, Talal Rahwan, Tomasz P Michalak, and Makoto Yokoo. Attachment centrality: An axiomatic approach to connectivity in networks. In Proceedings of the 2016 International Conference on Autonomous Agents & Multiagent Systems, pages 168-176. International Foundation for Autonomous Agents and Multiagent Systems, 2016. Google Scholar
  29. Oskar Skibski and Jadwiga Sosnowska. Axioms for distance-based centralities. In Thirty-Second AAAI Conference on Artificial Intelligence, 2018. Google Scholar
  30. Leslie G Valiant. The complexity of computing the permanent. Theoretical computer science, 8(2):189-201, 1979. Google Scholar
  31. Tomasz Wąs and Oskar Skibski. An axiomatization of the eigenvector and Katz centralities. In Thirty-Second AAAI Conference on Artificial Intelligence, 2018. Google Scholar
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail