A Variant of Updating PageRank in Evolving Tree Graphs

Perturbed Markov Chains and Information Networks

“…Here we define a phase space X corresponding to P 0 as X = X (1) ∪ X (2) , where X (1) = {1, 2, 3, 4} and X (2) = {5, 6, 7, 8}. The corresponding matrices of transition probabilities for the two ergodic classes are, respectively, P 0,1 and P 0,2 , where P 0,1 = 0 1 0 0 We are going to get the second order asymptotic expansion for stationary probabilities π ε,k , k ∈ X given by relation (59).…”

“…(2) ε,k , k ∈ X (2) . Then, these expansions can be transformed in the corresponding expansions for π ε,k , k ∈ X, using relations π ε,k = f (g) d π (g) ε,k , k ∈ X (g) , g = 1, 2 and taking into account that, in this case, probabilities f…”

“…ε,k for phase space X (2) can be computed. The eigenvalues corresponding to P 0,2 are, where i 2 = −1.…”

“…The eigenvalues corresponding to P 0,2 are, where i 2 = −1. Hence, from relation (56), we obtain eigenvalues decomposition of P 0,2 , for k ∈ X (2) , n ≥ 1, as (149)…”

“…In addition, variants of PageRank in relation to some specific networks has been studied, e.g. in [8] and [9]; and also updating PageRank due to changes in some network is in literature, for instance, in [1] and [2].…”