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.

References

[1] Shvydun, S. (2025). Zoo of Centralities: Encyclopedia of Node Metrics in Complex Networks. arXiv: 2511.05122 https://doi.org/10.48550/arXiv.2511.05122
[2] Sheng, J., Dai, J., Wang, B., Duan, G., Long, J., Zhang, J., Guan, K., Hu, S., Chen, L. & Guan, W. (2020). Identifying influential nodes in complex networks based on global and local structure. Physica A: Statistical Mechanics and its Applications, 541, 123262. doi: 10.1016/j.physa.2019.123262.
[3] Jeh, G., & Widom, J. (2002). Simrank: a measure of structural-context similarity. In Proceedings of the eighth ACM SIGKDD international conference on Knowledge discovery and data mining (pp. 538-543). doi: 10.1145/775047.775126.