Random Walks on Complex Networks

Random walks on complex networks was investigated to derive an exact expression for the mean first-passage time (MFPT) between two modes. The random walk centrality C, which is the ratio between its coordination number and a characterstic relaxation time was introduced for each mode. It was shown that MFPT is determined by C. The relative speed by which a node receives and spreads information over the network in a random process was determined by the centrality of the node. The analysis was confirmed by the numerical simulations of an ensemble of random walkers moving on paradigmatic network models.