Random Walks on Complex Networks

Random Walks on Complex Networks

February 2, 2008 | Jae Dong Noh, Heiko Rieger
The paper investigates random walks on complex networks, focusing on scale-free (SF) networks characterized by a power-law degree distribution. The authors derive an exact formula for the mean first passage time (MFPT) between two nodes, which is influenced by the random walk centrality (RWC) of each node. RWC is defined as the ratio of the node's coordination number to its characteristic relaxation time and determines the relative speed at which information spreads from one node to another. Numerical simulations on paradigmatic network models, including the Barabási-Albert (BA) network and a hierarchical network, confirm the analytical predictions. The results show that nodes with higher RWC values are visited earlier by random walkers and receive more information, leading to a centralization of information in these nodes. This highlights the importance of managing nodes with high RWC values to prevent congestion in network transport processes.The paper investigates random walks on complex networks, focusing on scale-free (SF) networks characterized by a power-law degree distribution. The authors derive an exact formula for the mean first passage time (MFPT) between two nodes, which is influenced by the random walk centrality (RWC) of each node. RWC is defined as the ratio of the node's coordination number to its characteristic relaxation time and determines the relative speed at which information spreads from one node to another. Numerical simulations on paradigmatic network models, including the Barabási-Albert (BA) network and a hierarchical network, confirm the analytical predictions. The results show that nodes with higher RWC values are visited earlier by random walkers and receive more information, leading to a centralization of information in these nodes. This highlights the importance of managing nodes with high RWC values to prevent congestion in network transport processes.
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Understanding Random walks on complex networks.