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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
References
Balakrishnan, R.: The energy of a graph. Linear Algebra Appl. 387, 287–295 (2004)
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)
Bonacich, P.: Power and centrality: a family of measures. Am. J. Sociol. 92(5), 1170–1182 (1987)
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)
Erdős, P., Rényi, A.: On the evolution of random graphs. Publ. Math. Inst. Hung. Acad. Sci. 5(1), 17–60 (1960)
Gutman, I.: The energy of a graph: old and new results. In: Algebraic Combinatorics and Applications, pp. 196–211. Springer (2001)
Gutman, I., Furtula, B., Bozkurt, Ş.B.: On randić energy. Linear Algebra Appl. 442, 50–57 (2014)
Gutman, I., Kiani, D., Mirzakhah, M., Zhou, B.: On incidence energy of a graph. Linear Algebra Appl. 431(8), 1223–1233 (2009)
Gutman, I., Zhou, B.: Laplacian energy of a graph. Linear Algebra Appl. 414(1), 29–37 (2006)
Holme, P., Kim, B.J.: Growing scale-free networks with tunable clustering. Phys. Rev. E 65(2), 026107 (2002)
Ilić, A.: Distance spectra and distance energy of integral circulant graphs. Linear Algebra Appl. 433(5), 1005–1014 (2010)
Kajdanowicz, T., Morzy, M.: Using graph and vertex entropy to compare empirical graphs with theoretical graph models. Entropy 18(9), 320 (2016)
Morduch, J., Haley, B.: Analysis of the effects of microfinance on poverty reduction. NYU Wagner Working Paper 1014, New York (2002)
Morzy, M., Kajdanowicz, T.: Graph energies of egocentric networks and their correlation with vertex centrality measures. Entropy 20(12), 916 (2018)
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)
Van Mieghem, P.: Graph Spectra for Complex Networks. Cambridge University Press, Cambridge (2010)
Acknowledgements
This work was supported by the National Science Centre, Poland, the decision no. 2016/23/B/ST6/03962.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Morzy, M., Wójtowicz, T. (2020). Stable and Uniform Resource Allocation Strategies for Network Processes Using Vertex Energy Gradients. In: Cherifi, H., Gaito, S., Mendes, J., Moro, E., Rocha, L. (eds) Complex Networks and Their Applications VIII. COMPLEX NETWORKS 2019. Studies in Computational Intelligence, vol 881. Springer, Cham. https://doi.org/10.1007/978-3-030-36687-2_58
Download citation
DOI: https://doi.org/10.1007/978-3-030-36687-2_58
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-36686-5
Online ISBN: 978-3-030-36687-2
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)