Random Multi-Hopper Model. Super-Fast Random Walks on Graphs

  title={Random Multi-Hopper Model. Super-Fast Random Walks on Graphs},
  author={Ernesto Estrada and Jean-Charles Delvenne and Naomichi Hatano and Jos{\'e} L. Mateos and Ralf Metzler and Alejandro P. Riascos and Michael T. Schaub},
  journal={J. Complex Networks},
We develop a model for a random walker with long-range hops on general graphs. This random multi-hopper jumps from a node to any other node in the graph with a probability that decays as a function of the shortest-path distance between the two nodes. We consider here two decaying functions in the form of the Laplace and Mellin transforms of the shortest-path distances. Remarkably, when the parameters of these transforms approach zero asymptotically, the multi-hopper's hitting times between any… 

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