Cross-clique connectivity
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.