Document Open Access Logo

Absolute Expressiveness of Subgraph-Based Centrality Measures

Authors Andreas Pieris , Jorge Salas



PDF
Thumbnail PDF

File

LIPIcs.ICDT.2023.9.pdf
  • Filesize: 0.79 MB
  • 18 pages

Document Identifiers

Author Details

Andreas Pieris
  • University of Edinburgh, UK
  • University of Cyprus, Nicosia, Cyprus
Jorge Salas
  • Pontificia Universidad Católica de Chile, Santiago, Chile
  • University of Edinburgh, UK

Cite AsGet BibTex

Andreas Pieris and Jorge Salas. Absolute Expressiveness of Subgraph-Based Centrality Measures. In 26th International Conference on Database Theory (ICDT 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 255, pp. 9:1-9:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.ICDT.2023.9

Abstract

In graph-based applications, a common task is to pinpoint the most important or "central" vertex in a (directed or undirected) graph, or rank the vertices of a graph according to their importance. To this end, a plethora of so-called centrality measures have been proposed in the literature. Such measures assess which vertices in a graph are the most important ones by analyzing the structure of the underlying graph. A family of centrality measures that are suited for graph databases has been recently proposed by relying on the following simple principle: the importance of a vertex in a graph is relative to the number of "relevant" connected subgraphs surrounding it; we refer to the members of this family as subgraph-based centrality measures. Although it has been shown that such measures enjoy several favourable properties, their absolute expressiveness remains largely unexplored. The goal of this work is to precisely characterize the absolute expressiveness of the family of subgraph-based centrality measures by considering both directed and undirected graphs. To this end, we characterize when an arbitrary centrality measure is a subgraph-based one, or a subgraph-based measure relative to the induced ranking. These characterizations provide us with technical tools that allow us to determine whether well-established centrality measures are subgraph-based. Such a classification, apart from being interesting in its own right, gives useful insights on the structural similarities and differences among existing centrality measures.

Subject Classification

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

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. Phillip Bonacich. Power and centrality: A family of measures. American journal of sociology, 92(5):1170-1182, 1987. Google Scholar
  3. Stephen P. Borgatti and Martin G. Everett. A graph-theoretic perspective on centrality. Soc. Networks, 28(4):466-484, 2006. Google Scholar
  4. Zoltán Dezső and Albert-László Barabási. Halting viruses in scale-free networks. Phys. Rev. E, 65:055103, 2002. Google Scholar
  5. Aidan Hogan, Andreas Harth, Jürgen Umbrich, Sheila Kinsella, Axel Polleres, and Stefan Decker. Searching and browsing linked data with SWSE: the semantic web search engine. J. Web Semant., 9(4):365-401, 2011. Google Scholar
  6. Xinyu Huang, Dongming Chen, Dongqi Wang, and Tao Ren. Identifying influencers in social networks. Entropy, 22(4):450, 2020. Google Scholar
  7. Gábor Iván and Vince Grolmusz. When the Web meets the cell: using personalized PageRank for analyzing protein interaction networks. Bioinformatics, 27(3):405-407, 2010. Google Scholar
  8. Mitri Kitti. Axioms for centrality scoring with principal eigenvectors. Social Choice and Welfare, 46(3):639-653, 2016. Google Scholar
  9. José-Lázaro Martínez-Rodríguez, Aidan Hogan, and Ivan López-Arévalo. Information extraction meets the semantic web: A survey. Semantic Web, 11(2):255-335, 2020. Google Scholar
  10. Leonid Mirsky. Transversal Theory: An Account of Some Aspects of Combinatorial Mathematics. Academic Press, 1971. Google Scholar
  11. Mark Newman. Networks. Oxford University Press, 2018. Google Scholar
  12. Lawrence Page, Sergey Brin, Rajeev Motwani, and Terry Winograd. The pagerank citation ranking: Bringing order to the web. Technical Report 1999-66, Stanford InfoLab, 1999. Google Scholar
  13. Richard Rado. Axiomatic treatment of rank in infinite sets. Canad. J. Math., pages 337-343, 1949. Google Scholar
  14. Cristian Riveros and Jorge Salas. A family of centrality measures for graph data based on subgraphs. In ICDT, pages 23:1-23:18, 2020. Google Scholar
  15. Gert Sabidussi. The centrality index of a graph. Psychometrika, 31(4):581-603, 1966. Google Scholar
  16. Alfonso Shimbel. Structural parameters of communication networks. Bull. Math. Biophysics, 15:501-507, 1953. Google Scholar
  17. Edward Szpilrajn. Sur l'extension de l'ordre partiel. Fundamenta Matematicae, 16:386-389, 1930. Google Scholar
  18. René van den Brink and Robert P. Gilles. Measuring domination in directed networks. Social Networks, 22(2):141-157, 2000. Google Scholar
  19. Tomasz Was and Oskar Skibski. Axiomatization of the pagerank centrality. In IJCAI, pages 3898-3904, 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