  Centrality measures are fundamental tools of network analysis as they
highlight the key actors within the network. This study focuses on a newly
proposed centrality measure, Expected Force (EF), and its use in identifying
spreaders in network-based epidemic models. We found that EF effectively
predicts the spreading power of nodes and identifies key nodes and immunization
targets. However, its high computational cost presents a challenge for its use
in large networks. To overcome this limitation, we propose two parallel
scalable algorithms for computing EF scores: the first algorithm is based on
the original formulation, while the second one focuses on a cluster-centric
approach to improve efficiency and scalability. Our implementations
significantly reduce computation time, allowing for the detection of key nodes
at large scales. Performance analysis on synthetic and real-world networks
demonstrates that the GPU implementation of our algorithm can efficiently scale
to networks with up to 44 million edges by exploiting modern parallel
architectures, achieving speed-ups of up to 300x, and 50x on average, compared
to the simple parallel solution.
