Comm Centrality
Comm centrality
is a community-based centrality measure that quantifies a node’s importance by combining its intra- and inter-community connectivity through a weighted formulation [2].
Assume that the network \(G\) has a community structure consisting of \(K > 1\) communities.
For a node \(i\) belonging to community \(C\), the Comm centrality \(c_{comm}(i)\) is defined as
\begin{equation*}
c_{comm}(i) = (1+μ_C) \left( \frac{d_i^{in}}{\max_{j \in C} d_j^{in}} \cdot R \right)
+ (1-μ_C) \left( \frac{d_i^{out}}{\max_{j \in C} d_j^{out}} \cdot R \right)^2,
\end{equation*}
where \(d_i^{in}\) is the number of links connecting node \(i\) to other nodes within the same community, \(d_i^{out}\) is the number of links from node \(i\) to nodes in other communities, and \(R\) is a scaling parameter.
The community mixing parameter \(μ_C\) is defined as
\begin{equation*}
μ_C = \frac{1}{|C|} \sum_{j \in C} \frac{d_j^{out}}{d_j},
\end{equation*}
representing the average proportion of inter-community links within community \(C\).
Gupta et al. [2] suggest setting \(R = \max_{j \in C} d_j^{in}\).
Nodes with high Comm centrality values either have strong intra-community connectivity or act as key bridges between communities, depending on the structural mixing parameter \(μ_C\).