The cross-clique connectivity (CCC) quantifies how extensively a node participates in multiple cohesive groups within a network [2]. It is based on the idea that nodes belonging to several cliques (fully connected subgraphs) play a crucial role in linking otherwise separate dense regions of the network. Formally, the cross-clique connectivity of a node \(i\) is defined as\begin{equation*}c_{\text{ccc}}(i) = \left| \left\{ C \subseteq \mathcal{N}: i \in C,\, C \text{ is a clique and } |C| \ge 3 \right\} \right|,\end{equation*}that is, the number of cliques of size at least three that include node \(i\). Nodes with high \(c_{\text{ccc}}(i)\) values are referred to as highly cross-connected nodes. Such nodes serve as structural bridges between tightly connected groups, facilitating interactions and information flow across different cohesive communities within the network.

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] Faghani, M. R., & Nguyen, U. T. (2013). A study of XSS worm propagation and detection mechanisms in online social networks. IEEE transactions on information forensics and security, 8(11), 1815-1826. doi: 10.1109/TIFS.2013.2280884.