@article{EstradaDelvenneHatanoetal.2018,
  author    = {Estrada, Ernesto and Delvenne, Jean-Charles and Hatano, Naomichi and Mateos, Jose L. and Metzler, Ralf and Riascos, Alejandro P. and Schaub, Michael T.},
  title     = {Random multi-hopper model},
  series = {Journal of Complex Networks},
  volume    = {6},
  journal   = {Journal of Complex Networks},
  number    = {3},
  publisher = {Oxford Univ. Press},
  address   = {Oxford},
  issn      = {2051-1310},
  doi       = {10.1093/comnet/cnx043},
  pages     = {382 -- 403},
  year      = {2018},
  abstract  = {We develop a mathematical model considering a random walker with long-range hops on arbitrary graphs. The random multi-hopper can jump to any node of the graph from an initial position, with a probability that decays as a function of the shortest-path distance between the two nodes in the graph. We consider here two decaying functions in the form of Laplace and Mellin transforms of the shortest-path distances. We prove that when the parameters of these transforms approach zero asymptotically, the hitting time in the multi-hopper approaches the minimum possible value for a normal random walker. We show by computational experiments that the multi-hopper explores a graph with clusters or skewed degree distributions more efficiently than a normal random walker. We provide computational evidences of the advantages of the random multi-hopper model with respect to the normal random walk by studying deterministic, random and real-world networks.},
  language  = {en}
}