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Random walks on graphs

Author

Listed:
  • Göbel, F.
  • Jagers, A. A.

Abstract

In this paper the following Markov chains are considered: the state space is the set of vertices of a connected graph, and for each vertex the transition is always to an adjacent vertex, such that each of the adjacent vertices has the same probability. Detailed results are given on the expectation of recurrence times, of first-entrance times, and of symmetrized first-entrance times (called commuting times). The problem of characterizing all connected graphs for which the commuting time is constant over all pairs of adjacent vertices is solved almost completely.

Suggested Citation

  • Göbel, F. & Jagers, A. A., 1974. "Random walks on graphs," Stochastic Processes and their Applications, Elsevier, vol. 2(4), pages 311-336, October.
    • Handle: RePEc:eee:spapps:v:2:y:1974:i:4:p:311-336
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    Citations

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    Cited by:

    1. Diala Wehbe & Nicolas Wicker, 2022. "Convergence Details About k-DPP Monte-Carlo Sampling for Large Graphs," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(1), pages 188-203, May.
    2. Guo, Wei-Feng & Zhang, Shao-Wu, 2016. "A general method of community detection by identifying community centers with affinity propagation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 447(C), pages 508-519.
    3. Lin, Dan & Wu, Jiajing & Xuan, Qi & Tse, Chi K., 2022. "Ethereum transaction tracking: Inferring evolution of transaction networks via link prediction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 600(C).
    4. Kumar, Ajay & Singh, Shashank Sheshar & Singh, Kuldeep & Biswas, Bhaskar, 2020. "Link prediction techniques, applications, and performance: A survey," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 553(C).
    5. Silver, Grant & Akbarzadeh, Meisam & Estrada, Ernesto, 2018. "Tuned communicability metrics in networks. The case of alternative routes for urban traffic," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 402-413.
    6. Kivimäki, Ilkka & Shimbo, Masashi & Saerens, Marco, 2014. "Developments in the theory of randomized shortest paths with a comparison of graph node distances," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 393(C), pages 600-616.
    7. Palacios, JoséLuis & Renom, JoséMiguel, 1998. "Random walks on edge transitive graphs," Statistics & Probability Letters, Elsevier, vol. 37(1), pages 29-34, January.
    8. Mueller, Falko, 2023. "Link and edge weight prediction in air transport networks — An RNN approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 613(C).
    9. Feng, Lihua & Liu, Weijun & Lu, Lu & Wang, Wei & Yu, Guihai, 2022. "The access time of random walks on trees with given partition," Applied Mathematics and Computation, Elsevier, vol. 427(C).
    10. Ranjan, Gyan & Zhang, Zhi-Li, 2013. "Geometry of complex networks and topological centrality," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(17), pages 3833-3845.
    11. Pei, Panpan & Liu, Bo & Jiao, Licheng, 2017. "Link prediction in complex networks based on an information allocation index," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 470(C), pages 1-11.

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