## Abstract

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## Notes

1. 1.

We have to note that the focus of Tong et al. (2010) is to identify which nodes should be removed from a network to make it more robust against epidemic spread. In contrast, our goal is to identify the nodes that make the graph more susceptible to the (viral) spread of information when injecting new links adjacent to these nodes.

2. 2.

At the beginning of the algorithm, since the set $$S$$ does not contain an item, the matrix $$H$$ is also empty.

3. 3.

Each $$p_{vw}$$ is computed by dividing the sum of all weights of incoming ties to $$w$$.

4. 4.

Please note that several other probability distributions do not satisfy this property, by having an unbounded support.

5. 5.

Notice that in Eq. 4, the truncation of weight $$W_{vw}$$ into the interval $$[0,1]$$ results in an activation probability $$p'_{vw}$$. The reasoning behind this truncation is as follows: in IC, the attempt of a user $$v$$ to activate a neighbor user $$w$$ is implemented by generating a random number $$r$$ that follows uniform distribution in the interval $$[0,1]$$. The value of $$r$$ is then compared to the weight $$W_{vw}$$. User $$w$$ becomes activated, if $$r < W_{vw}$$. Thus, negative values of the weight $$W_{vw}$$ correspond to an activation probability $$p'_{vw} = 0$$, since in this case it always holds that $$r \nless W_{vw}$$. Similarly, values of the weight $$W_{vw}$$ that are higher than 1, correspond to an activation probability $$p'_{vw} = 1$$, since in this case it always holds that $$r < W_{vw}$$.

6. 6.
7. 7.

The small difference in the $$\alpha$$ values used with IC and LT (2 and 1.78, respectively) is justified by the results in Fig. 1a, b, which refer to the performance of the SenderRank baseline and, thus, the small discrepancies in the number of activations are due to the subtle differences between the two diffusion models themselves. We selected the $$\alpha$$ value for LT accordingly (based on linear interpolation) so that we can more clearly identify in the sequel the performance gains due to link injection, after having first aligned the performance of the SenderRank baseline w.r.t. the two diffusion models.

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Correspondence to Stefanos Antaris.

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Antaris, S., Rafailidis, D. & Nanopoulos, A. Link injection for boosting information spread in social networks. Soc. Netw. Anal. Min. 4, 236 (2014). https://doi.org/10.1007/s13278-014-0236-y