Advertisement

Stable and Uniform Resource Allocation Strategies for Network Processes Using Vertex Energy Gradients

  • Mikołaj MorzyEmail author
  • Tomi Wójtowicz
Conference paper
Part of the Studies in Computational Intelligence book series (SCI, volume 881)

Abstract

In this paper we investigate the effects of initial resource allocation strategy on the stability and uniformity of resource distribution in network-driven processes. We assume that the resource exchange process is controlled by the topology of the underlying network and we are looking for the initial allocation strategy which produces low variance and uniformity of resource distribution.

The results of experiments conducted on synthetic and empirical networks are surprising. We find that allocation strategies based on vertex energy outperform other strategies substantially for a wide spectrum of considered network topologies. In particular, we introduce for the first time the notion of vertex energy gradients and we use these gradients to compute eigenvalue centralities of vertices. Allocation of resources proportional to these centralities results in very stable and uniform distributions for resource exchange processes.

Keywords

Resource allocation Vertex energy Network process 

Notes

Acknowledgements

This work was supported by the National Science Centre, Poland, the decision no. 2016/23/B/ST6/03962.

References

  1. 1.
    Balakrishnan, R.: The energy of a graph. Linear Algebra Appl. 387, 287–295 (2004)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Bollobás, B., Borgs, C., Chayes, J., Riordan, O.: Directed scale-free graphs. In: Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 132–139. Society for Industrial and Applied Mathematics (2003)Google Scholar
  3. 3.
    Bonacich, P.: Power and centrality: a family of measures. Am. J. Sociol. 92(5), 1170–1182 (1987)CrossRefGoogle Scholar
  4. 4.
    Bozkurt, S.B., Güngör, A.D., Gutman, I., Cevik, A.S.: Randic matrix and randic energy. MATCH Commun. Math. Comput. Chem 64, 239–250 (2010)MathSciNetzbMATHGoogle Scholar
  5. 5.
    Erdős, P., Rényi, A.: On the evolution of random graphs. Publ. Math. Inst. Hung. Acad. Sci. 5(1), 17–60 (1960)MathSciNetzbMATHGoogle Scholar
  6. 6.
    Gutman, I.: The energy of a graph: old and new results. In: Algebraic Combinatorics and Applications, pp. 196–211. Springer (2001)Google Scholar
  7. 7.
    Gutman, I., Furtula, B., Bozkurt, Ş.B.: On randić energy. Linear Algebra Appl. 442, 50–57 (2014)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Gutman, I., Kiani, D., Mirzakhah, M., Zhou, B.: On incidence energy of a graph. Linear Algebra Appl. 431(8), 1223–1233 (2009)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Gutman, I., Zhou, B.: Laplacian energy of a graph. Linear Algebra Appl. 414(1), 29–37 (2006)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Holme, P., Kim, B.J.: Growing scale-free networks with tunable clustering. Phys. Rev. E 65(2), 026107 (2002)CrossRefGoogle Scholar
  11. 11.
    Ilić, A.: Distance spectra and distance energy of integral circulant graphs. Linear Algebra Appl. 433(5), 1005–1014 (2010)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Kajdanowicz, T., Morzy, M.: Using graph and vertex entropy to compare empirical graphs with theoretical graph models. Entropy 18(9), 320 (2016)CrossRefGoogle Scholar
  13. 13.
    Morduch, J., Haley, B.: Analysis of the effects of microfinance on poverty reduction. NYU Wagner Working Paper 1014, New York (2002)Google Scholar
  14. 14.
    Morzy, M., Kajdanowicz, T.: Graph energies of egocentric networks and their correlation with vertex centrality measures. Entropy 20(12), 916 (2018)CrossRefGoogle Scholar
  15. 15.
    Peterson, N.R., Pittel, B.: Distance between two random k-out digraphs, with and without preferential attachment. Adv. Appl. Probab. 47(3), 858–879 (2015)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Van Mieghem, P.: Graph Spectra for Complex Networks. Cambridge University Press, Cambridge (2010)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Institute of Computer SciencePoznan University of TechnologyPoznanPoland

Personalised recommendations