Kemeny's constant and global mean first passage time of random walks on octagonal cell network

This paper investigates the random walks of octagonal cell network. By using the Laplacian spectrum method, we obtain the mean first passage time (tau)$$ \left(\tau \right) $$ and Kemeny's constant (omega)$$ \left(\Omega \right) $$ between nodes. On one hand, the mean first passage time (tau)$$ \left(\tau \right) $$ is explicitly studied in terms of the eigenvalues of a Laplacian matrix. On the other hand, Kemeny's constant (omega)$$ \left(\Omega \right) $$ is introduced to measure node strength and to determine the scaling of the random walks. We provide an explicit expression of Kemeny's constant and mean first passage time for octagonal cell network, by their Laplacian eigenvalues and the correlation among roots of characteristic polynomial. Based on the achieved results, comparative studies are also performed for tau$$ \tau $$ and omega$$ \Omega $$. This work also deliver an inclusive approach for exploring random walks of networks, particularly biased random walks, which likewise support to better understand and tackle some practical problems such as search and routing on networks.

Automated summary

This paper investigates the random walks of octagonal cell network by using the Laplacian spectrum method. The mean first passage time (τ) and Kemeny's constant (Ω) between nodes are obtained. The mean first passage time (τ) is explicitly studied in terms of the eigenvalues of a Laplacian matrix, while Kemeny's constant (Ω) is introduced to measure node strength and determine the scaling of the random walks. An explicit expression of Kemeny's constant and mean first passage time for octagonal cell network is provided based on Laplacian eigenvalues and the correlation among roots of characteristic polynomial. Comparative studies are also performed for τ and Ω based on the achieved results. This work also delivers an inclusive approach for exploring random walks of networks, particularly biased random walks, which can help better understand and tackle practical problems such as search and routing on networks.