Redundancy measure
The
redundancy measure
, originally proposed in [2], is a simplified version of Burt's redundancy [3]. The redundancy \(c_r(i)\) of a node \(i\) quantifies the average number of connections that a neighbor of \(i\) has to other neighbors of \(i\), and is defined as
\begin{equation*}
c_r(i) =
\begin{cases}
\dfrac{\sum_{j \in \mathcal{N}(i)} \sum_{\substack{k \in \mathcal{N}(i), \ k \neq j}} a_{jk}}{d_i}, & \text{if } d_i > 1, \\
0, & \text{otherwise,}
\end{cases}
\end{equation*}
where \(\mathcal{N}(i)\) denotes the set of neighbors of node \(i\), and \(d_i = |\mathcal{N}(i)|\) is the degree of node \(i\). As shown by Newman [4], the redundancy measure is related to the clustering coefficient \(c_{cl}(i)\) via
\begin{equation*}
c_r(i) = c_{cl}(i) \, (d_i - 1).
\end{equation*}
The redundancy measure was later independently introduced as the
local average connectivity (LAC)
in [5].