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Improving the robustness of spatial networks by link addition: more and dispersed links perform better

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Abstract

It is an effective way to improve network robustness by adding connectivity links. Although some addition strategies have been proposed, the addition cost in spatial networks is still missing. This paper adopts a geographical network model to investigate two different constraint scenarios, revealing better addition mechanisms, i.e., limited addition range (LAR) and limited addition length (LAL). In LAR scenario, f additional connections are added within a certain radius r, while only the total length \(\delta \) of added links is noticed in LAL scenario. With numerical analysis, some ordinary results are first obtained that the robustness of spatial networks improves as f or \(\delta \) increases, indicating that more links produce better effects. In LAR, adding long links also works effectively. Besides, a special case of LAR is proposed that adding links intensively for a few nodes, and results show that dispersed addition performs better. In LAL, for each \(\delta \), feasible solutions are categorized by different numbers of links \(n_\delta \), and it is found that large \(n_\delta \) has a significant impact on robustness even though \(\delta \) gets longer. Although adding either more or long links can improve the robustness of spatial networks, it can be concluded that adding more and short links dispersedly outperforms fewer and long ones intensively.

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References

  1. Albert, R., Jeong, H., Barabási, A.-L.: Error and attack tolerance of complex networks. Nature 406(6794), 378–382 (2000)

    Google Scholar 

  2. Buldyrev, S.V., Parshani, R., Paul, G., Stanley, H.E., Havlin, S.: Catastrophic cascade of failure in interdependent networks. Nature 464(15), 1025–1028 (2010)

    Google Scholar 

  3. Motter, A.E., Lai, Y.C.: Cascade-based attacks on complex networks. Phys. Rev. E 66(6), 065102 (2002)

    Google Scholar 

  4. Crucitti, P., Latora, V., Marchiori, M.: Model for cascading failures in complex networks. Phys. Rev. E 69(4), 045104 (2004)

    Google Scholar 

  5. Kinney, R., Crucitti, P., Albert, R., Latora, V.: Modeling cascading failures in the north american power grid. Eur. Phys. J. B 46(1), 101–107 (2005)

    Google Scholar 

  6. Wang, J.-W., Rong, L.-L.: Cascade-based attack vulnerability on the us power grid. Saf. Sci. 47(10), 1332–1336 (2009)

    Google Scholar 

  7. Xia, Y.X., Hill, D.J.: Attack vulnerability of complex communication networks. IEEE Trans. Circuits Syst. II Express Briefs 55(1), 65–69 (2008)

    Google Scholar 

  8. Guo, Y., Wang, Z.X., Luo, S.P., Wang, Y.: A cascading failure model for interdomain routing system. Int. J. Commun Syst 25(8), 1068–1076 (2012)

    Google Scholar 

  9. Zhang, J.H., Zhao, M.W., Liu, H.K., Xu, X.M.: Networked characteristics of the urban rail transit networks. Physica A 392(61), 1538–1546 (2013)

    Google Scholar 

  10. Ren, T., Wang, Y.F., Liu, M.M., Xu, Y.J.: Analysis of robustness of urban bus network. Chin. Phys. B 25(21), 020101 (2016)

    Google Scholar 

  11. Gao, J.X., Buldyrev, S.V., Stanley, H.E., Havlin, S.: Networks formed from interdependent networks. Nat. Phys. 8(1), 40–48 (2012)

    Google Scholar 

  12. Nguyen, D.T., Shen, Y., Thai, M.T.: Detecting critical nodes in interdependent power networks for vulnerability assessment. IEEE Trans. Smart Grid 4(1), 151–159 (2013)

    Google Scholar 

  13. Zhou, D., Stanley, H .E., DÁgostino, G., Scala, A.: Assortativity decreases the robustness of interdependent networks. Phys. Rev. E 86(6), 066103 (2012)

    Google Scholar 

  14. Shao, J., Buldyrev, S.V., Havlin, S., Stanley, H.E.: Cascade of failures in coupled network systems with multiple support-dependence relations. Phys. Rev. E 83(3), 036116 (2011)

    MathSciNet  Google Scholar 

  15. Parshani, R., Rozenblat, C., Ietri, D., Ducruet, C., Havlin, S.: Inter-similarity between coupled networks. Europhys. Lett. 92(6), 68002 (2011)

    Google Scholar 

  16. Parshani, R., Buldyrev, S.V., Havlin, S.: Interdependent networks: reducing the coupling strength leads to a change from a first to second order percolation transition. Phys. Rev. Lett. 105(4), 048701 (2010)

    Google Scholar 

  17. Cui, P., Zhu, P., Wang, K., Xun, P., Xia, Z.: Enhancing robustness of interdependent network by adding connectivity and dependence links. Physica A 497, 185–197 (2018)

    MathSciNet  Google Scholar 

  18. Cao, X.-B., Hong, C., Du, W.-B., Zhang, J.: Improving the network robustness against cascading failures by adding links. Chaos Solitons Fractals 57, 35–40 (2013)

    MATH  Google Scholar 

  19. Ji, X., Wang, B., Liu, D., Chen, G., Tang, F., Wei, D., Tu, L.: Improving interdependent networks robustness by adding connectivity links. Physica A 444, 9–19 (2016)

    Google Scholar 

  20. Wang, X., Cao, J., Li, R., Zhao, T.: A preferential attachment strategy for connectivity link addition strategy in improving the robustness of interdependent networks. Physica A 483, 412–422 (2017)

    Google Scholar 

  21. Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A 357(3–4), 593–612 (2005)

    Google Scholar 

  22. Jiang, Z., Liang, M., Guo, D.: Enhancing network performance by edge addition. Int. J. Mod. Phys. C 22(11), 1211–1226 (2011)

    Google Scholar 

  23. Li, L., Jia, Q.S., Wang, H.T., Yuan, R.X., Guan, X.H.: A systematic method for network topology reconfiguration with limited link additions. J. Netw. Comput. Appl. 35(6), 1979–1989 (2012)

    Google Scholar 

  24. Rayatidamavandi, M., Conlon, F., Rahnamay-Naeini, M.: Reducing network vulnerability to malicious attacks. In: International Conference on Computing, Networking and Communications, p. 17858299. IEEE, Maui (2018)

  25. Ma, J., Han, W., Guo, Q., Wang, Z., Zhang, S.: A link-adding strategy for transport efficiency of complex networks. Int. J. Mod. Phys. C 27(5), 1650054 (2016)

    MathSciNet  Google Scholar 

  26. Bai, Y., Liu, S., Zhang, Z.: Effective hybrid link-adding strategy to enhance network transport efficiency for scale-free networks. Int. J. Mod. Phys. C 28(8), 1750107 (2017)

    Google Scholar 

  27. Jialili, M., Yu, X.: Enhancing pinning controllability of complex networks through link rewiring. IEEE Trans. Circuits Syst. II 64(6), 690–694 (2017)

    Google Scholar 

  28. Wang, H., Mieghem, P.V.: Algebraic connectivity optimization via link addition. In: Proceedings of the 3rd International Conference on Bio-Inspired Models of Network, Information and Computing Systems, pp. 412–422. ICST, Hyogo (2008)

  29. Sydney, A., Scoglio, C., Gruenbacher, D.: Optimizing algebraic connectivity by edge rewiring. Appl. Math. Comput. 219, 5465–5479 (2013)

    MathSciNet  MATH  Google Scholar 

  30. Schultz, P., Peron, T., Eroglu, D., Stemler, T., Ávila, G.M.R., Rodrigues, F.A., Kurths, J.: Tweaking synchronization by connectivity modifications. Phys. Rev. E 93(6), 06211 (2016)

    Google Scholar 

  31. Wang, Y., Song, D., Gao, X., Qu, S.-X., Lai, Y.-C., Wang, X.: Effect of network structural perturbations on spiral wave patterns. Nonlinear Dyn. 93(3), 1671–1680 (2018)

    Google Scholar 

  32. Jalili, M., Yu, X.: Enhancement of synchronizability in networks with community structure through adding efficient inter-community links. IEEE Trans. Netw. Sci. Eng. 3(2), 106–116 (2016)

    MathSciNet  Google Scholar 

  33. Zeng, A., Lu, L., Zhou, T.: Manipulating directed networks for better synchronization. New J. Phys. 14, 083006 (2012)

    Google Scholar 

  34. Barnett, L., Di Paolo, E., Bullock, S.: Spatially embedded random networks. Phys. Rev. E 76(5), 056115 (2007)

    MathSciNet  Google Scholar 

  35. Bashan, A., Berezin, Y., Buldyrev, S.V., Havlin, S.: The extreme vulnerability of interdependent spatially embedded networks. Nat. Phys. 9(10), 667–672 (2013)

    Google Scholar 

  36. Dong, Z., Tian, M., Liang, J., Fang, Y., Lu, Y.: Research on the connection radius of dependency links in interdependent spatial networks against cascading failures. Physica A 513, 555–564 (2018)

    MathSciNet  Google Scholar 

  37. Schneidera, C.M., Moreirab, A.A., Andrade, J.S., Havlin, S., Herrmanna, H.J.: Mitigation of malicious attacks on networks. Proc. Natl. Acad. Sci. USA 108(10), 3838–3841 (2011)

    Google Scholar 

  38. Herrmanna, H.J., Schneidera, C.M., Moreirab, A.A., Andrade, J.S., Havlin, S.: Onion-like network topology enhances robustness against malicious attacks. Proc. Natl. Acad. Sci. USA 2011, P01027 (2011)

    Google Scholar 

  39. Barabási, A.L., Albert, R.: Emergence of scaling in random networks. Science 286(5439), 509–512 (1999)

    MathSciNet  MATH  Google Scholar 

  40. Watts, D.J., Strogatz, S.H.: Collective dynamics of ‘small-world’ networks. Nature 393(6684), 440–442 (1998)

    MATH  Google Scholar 

  41. Xu, X.-J., Zhang, X., Mendes, J.F.F.: Impacts of preference and geography on epidemic spreading. Phys. Rev. E 76(5), 056109 (2007)

    Google Scholar 

  42. Yook, S.-H., Hawoong, J., Barabási, A.-L.: Modeling the internet’s large-scale topology. Proc. Natl. Acad. Sci. USA 99(21), 13382–13386 (2002)

    Google Scholar 

  43. Casey, M.J.: Self-organization and topology control of infrastructure sensor networks. Ph.D. Thesis. University of Maryland, College Park (2005)

  44. Albert, R., Barabási, A.L.: Statistical mechanics of complex networks. Rev. Mod. Phys. 74(1), 47–97 (2002)

    MathSciNet  MATH  Google Scholar 

  45. Rozenfeld, A.F., Cohen, R., Ben Avraham, D., Havlin, S.: Scale-free networks on lattices. Phys. Rev. Lett. 89(21), 218701 (2002)

    Google Scholar 

  46. Danziger, M.M., Shekhtman, L.M., Berezin, Y., Havlin, S.: The effect of spatiality on multiplex networks. Europhys. Lett. 115(3), 36002 (2016)

    Google Scholar 

  47. Barthélemy, M.: Crossover from scale-free to spatial networks. Europhys. Lett. 63(6), 915–921 (2003)

    Google Scholar 

  48. Jost, J., Joy, M.P.: Evolving networks with distance preferences. Phys. Rev. E 66(3), 036126 (2002)

    Google Scholar 

  49. Hines, P., Blumsack, S., Sanchez, E.C., Barrows, C.: The topological and electrical structure of power grids. In: 43rd Hawaii International Conference on System Sciences, p. 11205846. IEEE, Honolulu (2010)

  50. Waman, B.M.: Routing of multipoint connections. IEEE J. Sel. Areas Commun. 6(9), 1617–1622 (1988)

    Google Scholar 

  51. Ouyang, M., Hong, L., Mao, Z.-J., Yu, M.-H., Qi, F.: A methodological approach to analyze vulnerability of interdependent infrastructures. Simul. Model. Pract. Theory 17(5), 817–828 (2009)

    Google Scholar 

  52. Yan, K.-S., Rong, L.-L., Li, Q.: Vulnerability analysis of interdependent spatially embedded infrastructure networks under localized attack. Mod. Phys. Lett. B 31(9), 1750089 (2017)

    Google Scholar 

  53. Wang, J., Jiang, C., Qian, J.: Robustness of interdependent networks with different link patterns against cascading failures. Physica A 393, 535–541 (2014)

    Google Scholar 

  54. Wu, Z.-X., Peng, G., Wang, W.-X., Chan, S., Wing-Ming, W.E.: Cascading failure spreading on weighted heterogeneous networks. J. Stat. Mech. 2008, P05013 (2008)

    Google Scholar 

  55. McAndrew, T.C., Danforth, C.M., Bagrow, J.P.: Robustness of spatial mircronetworks. Phys. Rev. E 91(4), 042813 (2015)

    Google Scholar 

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Acknowledgements

This work was partially supported by the National Natural Science Foundation of China (Nos. 51807143, 51707135), the China Postdoctoral Science Special Foundation (No. 2018T110797), the China Postdoctoral Science Foundation (No. 2017M612499) and the Fundamental Research Funds for the Central Universities (No. 413000057).

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Dong, Z., Tian, M., Tang, R. et al. Improving the robustness of spatial networks by link addition: more and dispersed links perform better. Nonlinear Dyn 100, 2287–2298 (2020). https://doi.org/10.1007/s11071-020-05607-5

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