Trust-PageRank
Trust-PageRank
combines the traditional PageRank algorithm with a trust-value that reflects the reliability of information transmission between nodes [2]. The trust-value \(T_{ij}\) from node \(i\) to its adjacent node \(j\) is defined as a weighted combination of a similarity ratio and a degree ratio:
\begin{equation*}
T_{ij} = (1-β) R_{s_{ij}} + β R_{d_{ij}},
\end{equation*}
where the degree ratio is
\begin{equation*}
R_{d_{ij}} = \frac{d_i}{\sum_{l \in \mathcal{N}(j)} d_l},
\end{equation*}
and the similarity ratio is
\begin{equation*}
R_{s_{ij}} = \frac{s_{ij}}{\sum_{l \in \mathcal{N}(j)} s_{jl}}.
\end{equation*}
The similarity \(s_{ij}\) between nodes \(i\) and \(j\) is computed using the SimRank algorithm [3]:
\begin{equation*}
s_{ij} =
\begin{cases}
1, & i = j, \\
\frac{C}{d_i d_j} \sum_{a \in \mathcal{N}(i)} \sum_{b \in \mathcal{N}(j)} s_{ab}, & i \neq j,
\end{cases}
\end{equation*}
where \(C\) is an attenuation factor.
Analogous to PageRank, the Trust-PageRank influence of node \(i\) at time \(t\) is defined as
\begin{equation*}
TPR(i,t) = \frac{1-α}{N} + α \sum_{j \in \mathcal{N}(i)} T_{ij} \, TPR(j,t-1),
\end{equation*}
where \(α\) is the damping (jump) probability. The Trust-PageRank centrality of node \(i\) is given by its influence \(TPR(i,t^*)\) when the network reaches a steady state (\(t^* \to \infty\)) or after a fixed number of iterations (\(t^* = t^{\mathrm{max}}\)).
Hence, Trust-PageRank integrates structural connectivity and node-level trust, assigning higher centrality to nodes that are both well-connected and linked to trustworthy neighbors, reflecting their importance and reliability in information propagation.