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.