Gravity model
The
gravity model
(originally proposed in [2] as the inverse-square law method), inspired by Newton’s law of gravitation, evaluates a node’s importance in spreading dynamics by incorporating both neighborhood and path information [3]. In this model, the degree of a node is regarded as its mass, while the shortest path length between two nodes represents their distance.
The centrality \(c_{\text{GM}}(i)\) of node \(i\) is defined as
\begin{equation*}
c_{\text{GM}}(i) = \sum_{j \neq i} \frac{d_i\,d_j}{d_{ij}^2},
\end{equation*}
where \(d_{ij}\) denotes the shortest path distance between nodes \(i\) and \(j\) and \(d_i\) represents the degree of \(i\).
According to the gravity model, a node with a larger degree (reflecting stronger local connectivity) and shorter average distances to other nodes (indicating higher global accessibility) is considered more influential in the network.