Mean Hitting Time of Q-subdivision Complex Networks

Identification of influential vertices in complex networks: A hitting time‐based approach

“…To calculate the Hitting Time ($$$ {T}_{ij} $$$) between vertices $$$ i $$$ and $$$ j $$$, the authors used the eigenpair of the normalized adjacency matrix of the initial graph G. They analyzed the evolution of the Mean first passage Time for two large real‐world networks as the networks dynamic with the q‐subdivision. The results demonstrate that the Hitting centrality is robust to network size 19 …”

“…In other words, the likelihood of transitioning between vertex $$$ i $$$ and vertex $$$ j $$$ is $$$ \frac{A_{ij}}{d_i} $$$. This stochastic walk on $$$ G $$$ can be considered as a Markov chain, and its transition probabilities are described by the matrix $$$ T={D}^{-1}A $$$, where $$$ D $$$ is Diagonal degree matrix and $$$ A $$$ is adjacency matrix and $$$ T $$$ is transition probability matrix, 19 where the entry in $$$ T $$$ is $$$ \frac{A_{ij}}{d_i} $$$.…”

“…The concept of the first‐passage time, as discussed in previous works, 19,20 plays a vital role in random walks. It quantifies the anticipated number of steps a walker needs to navigate from the starting vertex $$$ i $$$ to the ending vertex $$$ j $$$.…”

“…. This stochastic walk on G can be considered as a Markov chain, and its transition probabilities are described by the matrix T = D −1 A, where D is Diagonal degree matrix and A is adjacency matrix and T is transition probability matrix, 19 where the entry in T is…”