Fusion gravity model (FGM)
The
fusion gravity model
(FGM) is a variant of the traditional gravity model that integrates multiple node attributes to evaluate the influence of nodes in complex networks [2]. Specifically, the FGM score \(c_{FGM}(i)\) of node \(i\) is defined as
\begin{equation*}
c_{FGM}(i) = e_i \sum_{j \in \mathcal{N}^{(\leq r)}(i)} \frac{v_i v_j}{d_{ij}^2},
\end{equation*}
where \(\mathcal{N}^{(\leq r)}(i)\) denotes the set of nodes whose shortest path distance from node \(i\) is less than or equal to \(r\), \(d_{ij}\) is the shortest path distance between nodes \(i\) and \(j\), \(e_i\) represents the eigenvector centrality of node \(i\), and \(r\) is the radius of influence. Guo
et al.
[2] suggest setting \(r = 0.5 \langle d \rangle\), where \(\langle d \rangle\) is the average shortest path length in the network \(G\).
The
mass
\(v_i\) of node \(i\) is given by
\[
v_i = \frac{d_i}{\max_j d_j} + \frac{k_s(i)}{\max_j k_s(j)},
\]
where \(d_i\) and \(k_s(i)\) denote the degree and the \(k\)-shell index of node \(i\), respectively.
The FGM index is designed to identify influential nodes in a network by combining structural and positional attributes. Its effectiveness is typically evaluated using the Susceptible-Infected (SI) propagation model.