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Comparative Study of Random Walks with One-Step Memory on Complex Networks

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Complex Networks XIV (CompleNet 2023)

Abstract

We investigate searching efficiency of different kinds of random walk on complex networks which rely on local information and one-step memory. For the studied navigation strategies we obtained theoretical and numerical values for the graph mean first passage times as an indicator for the searching efficiency. The experiments with generated and real networks show that biasing based on inverse degree, persistence and local two-hop paths can lead to smaller searching times. Moreover, these biasing approaches can be combined to achieve a more robust random search strategy. Our findings can be applied in the modeling and solution of various real-world problems.

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References

  1. Austerweil, J., Abbott, J.T., Griffiths, T.: Human memory search as a random walk in a semantic network. In: Advances in Neural Information Processing Systems, vol. 25. Curran Associates, Inc. (2012)

    Google Scholar 

  2. Backstrom, L., Leskovec, J.: Supervised random walks: predicting and recommending links in social networks. In: Proceedings of the 4th ACM International Conference on Web Search and Data Mining, pp. 635–644 (2011)

    Google Scholar 

  3. Basnarkov, L., Mirchev, M., Kocarev, L.: Persistent random search on complex networks. In: Trajanov, D., Bakeva, V. (eds.) ICT Innovations 2017. CCIS, vol. 778, pp. 102–111. Springer, Cham (2017)

    Chapter  Google Scholar 

  4. Basnarkov, L., Mirchev, M., Kocarev, L.: Random walk with memory on complex networks. Phys. Rev. E 102(4), 042315 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  5. Berenbrink, P., Cooper, C., Elsässer, R., Radzik, T., Sauerwald, T.: Speeding up random walks with neighborhood exploration. In: Proceedings of the 21st Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 1422–1435. SIAM (2010)

    Google Scholar 

  6. Bonaventura, M., Nicosia, V., Latora, V.: Characteristic times of biased random walks on complex networks. Phys. Rev. E 89(1), 012803 (2014)

    Article  ADS  Google Scholar 

  7. Cao, X., Wang, Y., Li, C., Weng, T., Yang, H., Gu, C.: One-step memory random walk on complex networks: an efficient local navigation strategy. Fluct. Noise Lett. 20(05), 2150040 (2021)

    Article  ADS  Google Scholar 

  8. Carletti, T., Battiston, F., Cencetti, G., Fanelli, D.: Random walks on hypergraphs. Phys. Rev. E 101(2), 022308 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  9. Fronczak, A., Fronczak, P.: Biased random walks in complex networks: the role of local navigation rules. Phys. Rev. E 80(1), 016107 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  10. Glonek, M., Tuke, J., Mitchell, L., Bean, N.: Semi-supervised graph labelling reveals increasing partisanship in the united states congress. Appl. Netw. Sci. 4(1), 1–18 (2019)

    Article  Google Scholar 

  11. Goh, K.I., Cusick, M.E., Valle, D., Childs, B., Vidal, M., Barabási, A.L.: The human disease network. Proc. Natl. Acad. Sci. 104(21), 8685–8690 (2007)

    Article  ADS  Google Scholar 

  12. Grinstead, C.M., Snell, J.L.: Introduction to probability. American Mathematical Society (2012)

    Google Scholar 

  13. Grover, A., Leskovec, J.: Node2vec: scalable feature learning for networks. In: Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 855-864. ACM (2016)

    Google Scholar 

  14. Leskovec, J., Kleinberg, J., Faloutsos, C.: Graphs over time: densification laws, shrinking diameters and possible explanations. In: Proceedings of the 11th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 177–187. ACM (2005)

    Google Scholar 

  15. Leskovec, J., Sosič, R.: Snap: a general-purpose network analysis and graph-mining library. ACM Trans. Intell. Syst. Technol. 8(1), 1–20 (2016)

    Article  Google Scholar 

  16. Newman, M.E.: Finding community structure in networks using the eigenvectors of matrices. Phys. Rev. E 74(3), 036104 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  17. Nikolentzos, G., Vazirgiannis, M.: Random walk graph neural networks. Adv. Neural Inf. Process. Syst. 33, 16211–16222 (2020)

    Google Scholar 

  18. Noh, J.D., Rieger, H.: Random walks on complex networks. Phys. Rev. Lett. 92(11), 118701 (2004)

    Article  ADS  Google Scholar 

  19. Page, L., Brin, S., Motwani, R., Winograd, T.: The pagerank citation ranking: Bringing order to the web. Technical report, Stanford InfoLab (1999)

    Google Scholar 

  20. Patel, R., Carron, A., Bullo, F.: The hitting time of multiple random walks. SIAM J. Matrix Anal. Appl. 37(3), 933–954 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  21. Riascos, A.P., Boyer, D., Herringer, P., Mateos, J.L.: Random walks on networks with stochastic resetting. Phys. Rev. E 101(6), 062147 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  22. Rossi, R.A., Ahmed, N.K.: The network data repository with interactive graph analytics and visualization. In: Proceedings of the 29th AAAI Conference on Artificial Intelligence (2015). https://networkrepository.com/

  23. Rozemberczki, B., Davies, R., Sarkar, R., Sutton, C.: Gemsec: graph embedding with self clustering. In: Proceedings of the 2019 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining, pp. 65–72. ACM (2019)

    Google Scholar 

  24. Seneta, E.: Non-negative Matrices and Markov Chains. Springer, Heidelberg (2006)

    MATH  Google Scholar 

  25. Šubelj, L., Bajec, M.: Robust network community detection using balanced propagation. Eur. Phys. J. B 81(3), 353–362 (2011)

    Article  ADS  Google Scholar 

  26. Tejedor, V., Bénichou, O., Voituriez, R.: Global mean first-passage times of random walks on complex networks. Phys. Rev. E 80(6), 065104 (2009)

    Article  ADS  Google Scholar 

  27. West, R., Leskovec, J.: Human wayfinding in information networks. In: Proceedings of the 21st International Conference on World Wide Web, pp. 619–628 (2012)

    Google Scholar 

  28. West, R., Pineau, J., Precup, D.: Wikispeedia: an online game for inferring semantic distances between concepts. In: 21st International Joint Conference on Artificial Intelligence (2009)

    Google Scholar 

  29. Zhu, X., Ghahramani, Z., Lafferty, J.D.: Semi-supervised learning using gaussian fields and harmonic functions. In: Proceedings of the 20th International Conference on Machine Learning (ICML-2003), pp. 912–919 (2003)

    Google Scholar 

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Acknowledgement

This research was partially supported by the Faculty of Computer Science and Engineering, at the Ss. Cyril and Methodius University in Skopje, N. Macedonia.

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Correspondence to Miroslav Mirchev .

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Mirchev, M., Basnarkov, L., Mishkovski, I. (2023). Comparative Study of Random Walks with One-Step Memory on Complex Networks. In: Teixeira, A.S., Botta, F., Mendes, J.F., Menezes, R., Mangioni, G. (eds) Complex Networks XIV. CompleNet 2023. Springer Proceedings in Complexity. Springer, Cham. https://doi.org/10.1007/978-3-031-28276-8_2

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