Science Advances

Supplementary Materials

The PDF file includes:

  • Section S1. Link epidemic importance and connected components
  • Section S2. Linearization of the ELE model
  • Section S3. Epidemic threshold
  • Section S4. Data description
  • Fig. S1. Ratio between the link epidemic importance IA of a link in a subnetwork A and the link epidemic importance IAB of a link that acts as the only bridge between subnetworks A and B.
  • Fig. S2. Epidemic containment for a network with 5000 nodes, power-law degree distribution of exponent 3, and average degree 〈k〉 = 6.
  • Fig. S3. Epidemic containment for a network with 5000 nodes, power-law degree distribution of exponent 3, high clustering coefficient, and average degree 〈k〉 = 6.
  • Fig. S4. Epidemic containment for the air transportation network.
  • Fig. S5. Epidemic containment for the general relativity collaborations network.
  • Fig. S6. Epidemic containment for an ER network with 5000 nodes and average degree 〈k〉 = 6.
  • Fig. S7. Epidemic containment for a network with 5000 nodes generated with a stochastic block model, with four blocks of 250 nodes, two blocks of 1000 nodes, and one block of 2000 nodes, average degree of 5, and mixing probability of 0.3.
  • Fig. S8. Epidemic containment for a network with 5000 nodes generated using the LFR algorithm, with average degree of 6, exponent of 3, and mixing probability of 0.1.
  • Fig. S9. Original air transportation network (top) and the results after a removal of 33.3% of the links using link epidemic importance (middle) and edge betweenness (bottom).
  • Fig. S10. Comparison of the number of connected components after total containment between the link epidemic importance strategy and the other four methods, calculated for the synthetic networks and parameters as in Fig. 4.
  • Fig. S11. Comparison of the number of connected components after total containment between the link epidemic importance and eigenscore strategies, calculated for the real networks and parameters as in Fig. 5.
  • Fig. S12. Graphical representation of the determination of the epidemic threshold.
  • Fig. S13. Computational time invested for each method to perform a single ranking and removal for BA networks ranging from 100 to 400,000 nodes, averaged over 36 repetitions.
  • Table S1. Structural characteristics of the 27 real networks obtained from the Network Repository ( http://networkrepository.com) and used in Fig. 6 and fig. S11.

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Other Supplementary Material for this manuscript includes the following:

  • Data file S1 (.graphml format). Air transportation network data.

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