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.

翻译：中心性度量是网络分析的基本工具，因为它们能够突出网络中的关键角色。本研究聚焦于一种新提出的中心性度量——期望力（EF），以及其在基于网络的流行病模型中识别传播者中的应用。我们发现EF能够有效预测节点的传播能力，并识别关键节点和免疫目标。然而，其高昂的计算成本对其在大型网络中的应用构成了挑战。为克服这一限制，我们提出了两种用于计算EF分数的并行可扩展算法：第一种算法基于原始公式，第二种算法则采用以簇为中心的方法以提高效率和可扩展性。我们的实现显著减少了计算时间，使得能够在大型规模下检测关键节点。在合成网络和真实世界网络上的性能分析表明，我们的算法的GPU实现通过利用现代并行架构，能够高效扩展到拥有多达4400万条边的网络，与简单并行解决方案相比，实现了高达300倍的加速，平均加速50倍。