Hide information measures how easily other nodes can reach a given node [2]. The hide information of node \(i\) is defined as\begin{equation*}c_{\mathcal{H}}(i) = \frac{1}{N} \sum_{j=1}^{N} S(j,i),\end{equation*}where\[S(j,i) = - \log_2 \sum_{\{p(j,i)\}} P[p(j,i)], \quad P[p(j,i)] = \frac{1}{k_j} \prod_{l \neq j \neq i \in p(j,i)} \frac{1}{k_l - 1}.\]Here, \(S(j,i)\) represents the amount of information required to locate node \(i\) starting from node \(j\), and \(P[p(j,i)]\) is the probability of following path \(p(j,i)\) when choosing neighbors uniformly at each step. A node with high hide information is easier to locate from other nodes. For example, in a star graph, the central hub has high hide information as it is easily reached from peripheral nodes [2].

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] Rosvall, M., Trusina, A., Minnhagen, P., & Sneppen, K. (2005). Networks and cities: An information perspective. Physical review letters, 94(2), 028701. doi: 10.1103/PhysRevLett.94.028701.