Local fuzzy information centrality (LFIC)
Local fuzzy information centrality
(LFIC) is a centrality measure for identifying influential nodes based on the local dimension of nodes and fuzzy theory [2].
The \textsc{LFIC} centrality \(c_{\textsc{LFIC}}(i)\) of node \(i\) is defined as
\[
c_{\textsc{LFIC}}(i) = \sum_{l=1}^{K} \frac{-p_i(l) \ln p_i(l)}{l^2},
\]
where \(l\) is the distance from the center node \(i\), and \(K\) is the maximal box size, defined as \(K = \lceil \max_j d_{ij} / 2 \rceil\). Here, \(p_i(l)\) is the probability associated with neighbor nodes at distance \(l\) from node \(i\):
\[
p_i(l) = \frac{1}{e} \frac{f_i(l)}{\sum_{l=1}^{K} f_i(l)},
\]
with
\[
f_i(l) = n_i(l) \, e^{-l^2 / K^2},
\]
where \(n_i(l)\) is the number of nodes whose shortest-path distance from node \(i\) equals \(l\).
Hence, LFIC combines local node structure with fuzzy weighting to capture the influence of nodes at varying distances from the center node.