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].