Skip to main content
SpringerLink
Log in

Comparative evaluation of community-aware centrality measures

  • Published:
Quality & Quantity Aims and scope Submit manuscript

Abstract

Influential nodes play a critical role in boosting or curbing spreading phenomena in complex networks. Numerous centrality measures have been proposed for identifying and ranking the nodes according to their importance. Classical centrality measures rely on various local or global properties of the nodes. They do not take into account the network community structure. Recently, a growing number of researches have shifted to community-aware centrality measures. Indeed, it is a ubiquitous feature in a vast majority of real-world networks. In the literature, the focus is on designing community-aware centrality measures. However, up to now, there is no systematic evaluation of their effectiveness. This study fills this gap. It allows answering which community-aware centrality measure should be used in practical situations. We investigate seven influential community-aware centrality measures in an epidemic spreading process scenario using the Susceptible–Infected–Recovered model on a set of fifteen real-world networks. Results show that generally, the correlation between community-aware centrality measures is low. Furthermore, in a multiple-spreader problem, when resources are available, targeting distant hubs using Modularity Vitality is more effective. However, with limited resources, diffusion expands better through bridges, especially in networks with a medium or strong community structure.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

Data availability

The datasets used in this article are all freely accessible in the cited resources.

Code availability

The code of the following study is accessible via GitHub: https://github.com/StephanyRajeh/CompAnalysisCACM

References

  • Anderson, R.M., May, R.M.: Population biology of infectious diseases: part I. Nature 280(5721), 361–367 (1979)

    Article  Google Scholar 

  • Berahmand, K., Bouyer, A., Samadi, N.: A new local and multidimensional ranking measure to detect spreaders in social networks. Computing 101(11), 1711–1733 (2019)

    Article  Google Scholar 

  • Buckee, C., Noor, A., Sattenspiel, L.: Thinking clearly about social aspects of infectious disease transmission. Nature 595(7866), 205–213 (2021)

    Article  Google Scholar 

  • Cherifi, H., Palla, G., Szymanski, B.K., Lu, X.: On community structure in complex networks: challenges and opportunities. Appl. Netw. Sci. 4(1), 1–35 (2019)

    Article  Google Scholar 

  • Dorogovtsev, S.N., Goltsev, A.V., Mendes, J.F.F.: K-core organization of complex networks. Phys. Rev. Lett. 96(4), 040601 (2006)

    Article  Google Scholar 

  • Everett, M.G., Borgatti, S.P.: The centrality of groups and classes. J. Math. Sociol. 23(3), 181–201 (1999)

    Article  Google Scholar 

  • Everett, M.G., Borgatti, S.P.: Extending centrality. Models Methods Soc. Netw. Anal. 35(1), 57–76 (2005)

    Article  Google Scholar 

  • Ghalmane, Z., El Hassouni, M., Cherifi, H.: Immunization of networks with non-overlapping community structure. SNAM 9(1), 1–22 (2019)

    Google Scholar 

  • Girvan, M., Newman, M.E.: Community structure in social and biological networks. PNAS 99(12), 7821–7826 (2002)

    Article  Google Scholar 

  • Guimera, R., Amaral, L.A.N.: Functional cartography of complex metabolic networks. Nature 433(7028), 895–900 (2005)

    Article  Google Scholar 

  • Gupta, N., Singh, A., Cherifi, H.: Centrality measures for networks with community structure. Physica A 452, 46–59 (2016)

    Article  Google Scholar 

  • Ismail, S.S., Akil, K.A.K., Chulan, M., Sharif, N.: The susceptible-infected-recovered (SIR) model for viral marketing. In: AIP Conference Proceedings, 1, p. 030018. AIP Publishing LLC (2017)

  • Jebabli, M., Cherifi, H., Cherifi, C., Hamouda, A.: Community detection algorithm evaluation with ground-truth data. Physica A 492, 651–706 (2018)

    Article  Google Scholar 

  • Kitsak, M., Gallos, L.K., Havlin, S., Liljeros, F., Muchnik, L., Stanley, H.E., Makse, H.A.: Identification of influential spreaders in complex networks. Nat. Phys. 6(11), 888–893 (2010)

    Article  Google Scholar 

  • Kunegis, J.: Handbook of network analysis [konect–the koblenz network collection] (2014). arXiv:1402.5500

  • Lancichinetti, A., Kivelä, M., Saramäki, J., Fortunato, S.: Characterizing the community structure of complex networks. PLoS ONE 5(8), e11976 (2010)

    Article  Google Scholar 

  • Li, C., Li, Q., Van Mieghem, P., Stanley, H.E., Wang, H.: Correlation between centrality metrics and their application to the opinion model. Eur. Phys. J. B 88(3), 1–13 (2015)

    Article  Google Scholar 

  • Lü, L., Chen, D., Ren, X.L., Zhang, Q.M., Zhang, Y.C., Zhou, T.: Vital nodes identification in complex networks. Phys. Rep. 650, 1–63 (2016)

    Article  Google Scholar 

  • Luo, S.L., Gong, K., Kang, L.: Identifying influential spreaders of epidemics on community networks. arXiv:1601.07700 (2016)

  • Magelinski, T., Bartulovic, M., M. Carley, K.: Measuring node contribution to community structure with modularity vitality. IEEE Trans. Netw. Sci. Eng. 8(1), 707–723 (2021)

  • Nematzadeh, A., Ferrara, E., Flammini, A., Ahn, Y.Y.: Optimal network modularity for information diffusion. Phys. Rev. Lett. 113(8), 088701 (2014)

    Article  Google Scholar 

  • Newman, M.E.: Modularity and community structure in networks. Proc. Natl. Acad. Sci. 103(23), 8577–8582 (2006)

    Article  Google Scholar 

  • Nguyen, B.: Modelling cyber vulnerability using epidemic models. In: SIMULTECH, pp. 232–239 (2017)

  • Oldham, S., Fulcher, B., Parkes, L., Arnatkeviciūtė, A., Suo, C., Fornito, A.: Consistency and differences between centrality measures across distinct classes of networks. PLoS ONE 14(7) (2019)

  • Orman, G.K., Labatut, V., Cherifi, H.: On accuracy of community structure discovery algorithms (2011). arXiv:1112.4134

  • Orman, G.K., Labatut, V., Cherifi, H.: Comparative evaluation of community detection algorithms: a topological approach. J. Stat. Mech. 2012(08), P08001 (2012)

    Article  Google Scholar 

  • Orman, K., Labatut, V., Cherifi, H.: An empirical study of the relation between community structure and transitivity. In: Complex Networks, pp. 99–110. Springer, Berlin (2013)

  • Peixoto, T.P.: The netzschleuder network catalogue and repository (2020). https://networks.skewed.de/

  • Rajeh, S., Savonnet, M., Leclercq, E., Cherifi, H.: Interplay between hierarchy and centrality in complex networks. IEEE Access 8, 129717–129742 (2020a)

    Article  Google Scholar 

  • Rajeh, S., Savonnet, M., Leclercq, E., Cherifi, H.: Investigating centrality measures in social networks with community structure. In: International Conference on Complex Networks and Their Applications, pp. 211–222. Springer, Berlin (2020b)

  • Rajeh, S., Savonnet, M., Leclercq, E., Cherifi, H.: Characterizing the interactions between classical and community-aware centrality measures in complex networks. Sci. Rep. 11(1), 1–15 (2021a)

    Article  Google Scholar 

  • Rajeh, S., Savonnet, M., Leclercq, E., Cherifi, H.: Comparing community-aware centrality measures in online social networks. In: International Conference on Computational Data and Social Networks, pp. 279–290. Springer, Berlin (2021b)

  • Rajeh, S., Savonnet, M., Leclercq, E., Cherifi, H.: How correlated are community-aware and classical centrality measures in complex networks? In: International Conference on Complex Networks, pp. 120–132. Springer, Berlin (2021c)

  • Ronqui, J.R.F., Travieso, G.: Analyzing complex networks through correlations in centrality measurements. J. Stat. Mech. 2015(5), P05030 (2015)

    Article  Google Scholar 

  • Rossi, R.A., Ahmed, N.K.: The network data repository with interactive graph analytics and visualization. In: AAAI (2015)

  • Rosvall, M., Bergstrom, C.T.: Maps of random walks on complex networks reveal community structure. PNAS 105(4), 1118–1123 (2008)

    Article  Google Scholar 

  • Rozemberczki, B., Sarkar, R.: Characteristic functions on graphs: birds of a feather, from statistical descriptors to parametric models (2020)

  • Schoch, D., Valente, T.W., Brandes, U.: Correlations among centrality indices and a class of uniquely ranked graphs. Soc. Netw. 50, 46–54 (2017)

    Article  Google Scholar 

  • Toda, A.A.: Susceptible-infected-recovered (SIR) dynamics of covid-19 and economic impact (2020). arXiv:2003.11221

  • Tulu, M.M., Hou, R., Younas, T.: Identifying influential nodes based on community structure to speed up the dissemination of information in complex network. IEEE Access 6, 7390–7401 (2018)

    Article  Google Scholar 

  • Wang, G.X., Qin, T.G.: Impact of community structure on network efficiency and communicability. In: 2010 International Conference on Intelligent Computation Technology and Automation, vol. 2, pp. 485–488. IEEE (2010)

  • Wang, W., Liu, Q.H., Zhong, L.F., Tang, M., Gao, H., Stanley, H.E.: Predicting the epidemic threshold of the susceptible-infected-recovered model. Sci. Rep. 6(1), 1–12 (2016)

    Google Scholar 

  • Wharrie, S., Azizi, L., Altmann, E.G.: Micro-, meso-, macroscales: the effect of triangles on communities in networks. Phys. Rev. E 100(2), 022315 (2019)

    Article  Google Scholar 

  • Yang, Z., Algesheimer, R., Tessone, C.J.: A comparative analysis of community detection algorithms on artificial networks. Sci. Rep. 6(1), 30750 (2016). https://doi.org/10.1038/srep30750

    Article  Google Scholar 

  • Zhao, Z., Wang, X., Zhang, W., Zhu, Z.: A community-based approach to identifying influential spreaders. Entropy 17(4), 2228–2252 (2015)

    Article  Google Scholar 

Download references

Funding

Not applicable.

Author information

Authors and Affiliations

  1. Laboratoire d’Informatique de Bourgogne, University of Burgundy, Dijon, France

    Stephany Rajeh, Marinette Savonnet, Eric Leclercq & Hocine Cherifi

Authors
  1. Stephany Rajeh
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Marinette Savonnet
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Eric Leclercq
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Hocine Cherifi
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

All authors have contributed to this work. SR implemented the models and the analyses. All authors participated in the formulation and writing of this paper. All authors approved the final manuscript.

Corresponding author

Correspondence to Stephany Rajeh.

Ethics declarations

Conflict of interest

Author HC has served on the editorial board of Quality and Quantity. The authors declare that they have no competing interests.

Consent to participate

Not applicable.

Consent for publication

Not applicable.

Ethical approval

Not applicable.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary Information

Below is the link to the electronic supplementary material.

Electronic supplementary material 1 (PDF 5315 kb)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Rajeh, S., Savonnet, M., Leclercq, E. et al. Comparative evaluation of community-aware centrality measures. Qual Quant 57, 1273–1302 (2023). https://doi.org/10.1007/s11135-022-01416-7

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11135-022-01416-7

Keywords

Search

Navigation