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Figure 1
(Color online) Comparison of the information spread in networks with loops. (a) An artificial network; (b) the back tracking edge (red) that is neglected in Eq. (
Figure 2
(Color online) The principle eigenvalues of the remaining networks that are obtained by removing the edges attached to the influential nodes. (a) Airtraffic network; (b) Bitcoin network; (c) ca-HepTh network; (d) Reactome network.
Figure 3
(Color online) The evolving paths of the spread as a function of time. In the experiments, every node has a probability of 0.001 to be an infected node initially. The results are the average of 50 independent simulations. (a) Airtraffic network; (b) Bitcoin network; (c) ca-HepTh network; (d) Reactome network.
Figure 4
(Color online) The average distance between influential nodes. (a) Airtraffic network; (b) Bitcoin network;protect łinebreak (c) ca-HepTh network; (d) Reactome network.
| Network | $N$ | $E$ | $H$ | $r$ | $\langle~C~\rangle$ | $\langle~d~\rangle$ | Sparsity |
| Airtraffic | 1225 | 2399 | 1.87 | $-$0.0177 | 0.011 | 5.93 | $3.2\times10^{-3}$ |
| Bitcoin | 5880 | 21228 | 10.89 | $-$0.163 | 0.022 | 3.59 | $1.2\times10^{-3}$ |
| ca-HepTh | 5039 | 11346 | 2.03 | 0.195 | 0.101 | 6.54 | $8.9\times10^{-4}$ |
| Reactome | 3851 | 140106 | 1.99 | 0.316 | 0.508 | 0.508 | $1.9\times10^{-2}$ |
Data preparation. Extract the giant component of the original network and remove the isolate nodes and other small nodes clusters because nodes located in distinct clusters could not exchange information. |
Initialize the algorithm and calculate the importance of nodes based on Eq. ( |
Rank nodes based on the importance of nodes and choose the particular node with the largest importance score. |
If the size of influential nodes is smaller than $L$, remove the edges attached to the influential nodes and go to step 2; otherwise go to step 5. |
Return the index of the chosen influential nodes. |
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