  Numerous real-world systems, for instance, the communication platforms and
transportation systems, can be abstracted into complex networks. Containing
spreading dynamics (e.g., epidemic transmission and misinformation propagation)
in networked systems is a hot topic in multiple fronts. Most of the previous
strategies are based on the immunization of nodes. However, sometimes, these
node--based strategies can be impractical. For instance, in the train
transportation networks, it is dramatic to isolating train stations for flu
prevention. On the contrary, temporarily suspending some connections between
stations is more acceptable. Thus, we pay attention to the edge-based
containing strategy. In this study, we develop a theoretical framework to find
the optimal edge for containing the spreading of the
susceptible-infected-susceptible model on complex networks. In specific, by
performing a perturbation method to the discrete-Markovian-chain equations of
the SIS model, we derive a formula that approximately provides the decremental
outbreak size after the deactivation of a certain edge in the network. Then, we
determine the optimal edge by simply choosing the one with the largest
decremental outbreak size. Note that our proposed theoretical framework
incorporates the information of both network structure and spreading dynamics.
Finally, we test the performance of our method by extensive numerical
simulations. Results demonstrate that our strategy always outperforms other
strategies based only on structural properties (degree or edge betweenness
centrality). The theoretical framework in this study can be extended to other
spreading models and offers inspirations for further investigations on
edge-based immunization strategies.
