Stable Matching in Structured Networks

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9806)


Stable matching studies how to pair members of two sets with the objective to achieve a matching that satisfies all participating agents based on their preferences. In this research, we consider the case of matching in a social network where agents are not fully connected. We propose the concept of D-neighbourhood associated with connective costs to investigate the matching quality in four types of well-used networks. A matching algorithm is proposed based on the classical Gale-Shapley algorithm under constraints of network topology. Through experimental studies, we find that the matching outcomes in scale-free networks yield the best average utility with least connective costs comparing to other structured networks. This research provides insights for understanding matching behavior in social networks like marriage, trade, partnership, online social and job search.


Stable matching Structured networks D-neighbourhood Connective cost 



This work is supported by the National Science Foundation of China Nos. 61305047 and 61401012.


  1. Barabási, A.L., Albert, R.: Emergence of scaling in random networks. Science 286(5439), 509–512 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  2. Dijkstra, E.W.: A note on two problems in connection with graphs. Numerische Math. 1(1), 269–271 (1959)MathSciNetCrossRefzbMATHGoogle Scholar
  3. Erdös, P., Rényi, A.: On random graphs. Publicationes Math. 6(4), 290–297 (1959)zbMATHGoogle Scholar
  4. Gale, D.: College admissions and the stability of marriage. Am. Math. Mon. 69(5), 9–15 (2013)zbMATHGoogle Scholar
  5. Gale, D., Sotomayor, M.: Some remarks on the stable matching problem. Discrete Appl. Math. 11(3), 223–232 (1985)MathSciNetCrossRefzbMATHGoogle Scholar
  6. Gomez-Gardenes, J., Moreno, Y.: From scale-free to Erdos-Renyi networks. Phys. Rev. E 73(5), 056124 (2006)CrossRefGoogle Scholar
  7. Jackson, M.O.: Allocation rules for network games. Games Econ. Behav. 51(1), 128–154 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  8. Jackson, M.O., Watts, A.: The evolution of social and economic networks. J. Econ. Theory 106(2), 265–295 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  9. Kitsak, M., et al.: Betweenness centrality of fractal, nonfractal scale-free model networks, tests on real networks. Phys. Rev. E 75, 056115 (2007)Google Scholar
  10. Latora, V., Marchiori, M.: Efficient behavior of small-world networks. Phys. Rev. Lett. 87(19), 198701 (2001)CrossRefGoogle Scholar
  11. Li, Z., Qin, Z.: Impact of social network structure on social welfare and inequality. In: Pedrycz, W., Chen, S.-M. (eds.) Social Networks: A Framework of Computational Intelligence. SCI, vol. 526, pp. 123–144. Springer, Switzerland (2014)CrossRefGoogle Scholar
  12. Li, Z., Chang, Y.-H., Maheswaran, R.: Graph formation effects on social welfare and inequality in a networked resource game. In: Greenberg, A.M., Kennedy, W.G., Bos, N.D. (eds.) SBP 2013. LNCS, vol. 7812, pp. 221–230. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  13. Liu, Q., et al.: Stable matching with incomplete information. Econometrica 82(2), 541–587 (2014)MathSciNetCrossRefGoogle Scholar
  14. Moldovanu, B.: Two-sided matching-A study in game-theoretic modeling and analysis (Book Review). J. Econ. (1992)Google Scholar
  15. Nisan, N., et al.: Algorithmic Game Theory. Cambridge University Press, Cambridge (2007)CrossRefGoogle Scholar
  16. Roth, A.E., Sotomayor, M.A.O.: A Study in Game-theoretic Modeling and Analysis. Cambridge University Press, Cambridge (2006)Google Scholar
  17. Shoham, Y.: Computer science and game theory. Commun. ACM 51(8), 74–79 (2008)CrossRefGoogle Scholar
  18. Strogatz, S.H.: Exploring complex networks. Nature 410(2), 24–27 (2001)Google Scholar
  19. Wang, X., Jiang, Y.: The influence of the randomness on average path length. Adv. Mat. Res. 87(19), 198701 (2011)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Intelligent Computing and Machine Learning Lab, School of ASEEBeihang UniversityBeijingChina
  2. 2.School of Biological Science and Medical EngineeringBeihang UniversityBeijingChina

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