Community hub-bridge (CHB) measure
Community hub-bridge (CHB) measure
is a community-based centrality metric that evaluates the importance of a node by considering both its intra- and inter-community connections [2].
Assume that the network \(G\) has a community structure consisting of \(K > 1\) communities.
For a node \(i\) belonging to community \(C_k\), the CHB centrality \(c_{CHB}(i)\) is defined as
\begin{equation*}
c_{CHB}(i) = |C_k|\, d_i^{in} + d_i^{out} \sum_{l \neq k} \left( \lor_{j \in C_l} a_{ij} \right),
\end{equation*}
where \(d_i^{in}\) is the number of intra-community links of node \(i\) (connections within \(C_k\)), \(d_i^{out}\) is the number of inter-community links (connections to nodes in other communities), and \(\lor\) denotes the logical OR operator.
The expression \(\left( \lor_{j \in C_l} a_{ij} \right) = 1\) if and only if node \(i\) is connected to at least one node \(j\) in community \(C_l\); otherwise, it equals zero.
Nodes with high CHB values act as both
hubs
(densely connected within their own community) and
bridges
(linking multiple communities), making them crucial for information flow and inter-community connectivity.