In recent years, the graph embedding approach has drawn a lot of attention in the field of network representation and analytics, the purpose of which is to automatically encode network elements into a low-dimensional vector space by preserving certain structural properties. On this basis, downstream machine learning methods can be implemented to solve static network analytic tasks, for example, node clustering based on community-preserving embeddings. However, by focusing only on structural properties, it would be difficult to characterize and manipulate various dynamics operating on the network. In the field of complex networks, epidemic spreading is one of the most typical dynamics in networks, while network immunization is one of the effective methods to suppress the epidemics. Accordingly, in this paper, we present a dynamics-preserving graph embedding method (EpiEm) to preserve the property of epidemic dynamics on networks, i.e., the infectiousness and vulnerability of network nodes. Specifically, we first generate a set of propagation sequences through simulating the Susceptible-Infectious process on a network. Then, we learn node embeddings from an influence matrix using a singular value decomposition method. Finally, we show that the node embeddings can be used to solve epidemics-related community mining and network immunization problems. The experimental results in real-world networks show that the proposed embedding method outperforms several benchmark methods with respect to both community mining and network immunization. The proposed method offers new insights into the exploration of other collective dynamics in complex networks using the graph embedding approach, such as opinion formation in social networks.
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