DegreeDiscountIC and SingleDiscount

DegreeDiscountIC and SingleDiscount (Chen, Wang and Yang 2009) select spreaders for the independent-cascade model one at a time by the largest discounted degree. After each selection every unselected neighbor $v$ of the new seed gains one selected neighbor $t_v$, and its DegreeDiscountIC degree becomes $$dd_v = d_v - 2 t_v - (d_v - t_v)\, t_v\, p,$$ with propagation probability $p$. SingleDiscount uses $d_v - t_v$.

Usage

centrality_degree_discount(x, discount_p = 0.01, ...)

centrality_single_discount(x, ...)

Arguments

x: Network input accepted by centrality.
discount_p: Propagation probability $p$ for DegreeDiscountIC (default 0.01).
...: Further arguments to centrality, such as normalized.

Value

A named numeric vector with one score per node, in input node order.

Details

Every node is placed, and the selection order is returned as a score. The first node selected scores 1 and the last $1/n$, so scores lie in $(0, 1]$. Ties are broken by node order, which the source leaves open. Direction, edge weights and self-loops are ignored.

References

Chen, W., Wang, Y., & Yang, S. (2009). Efficient influence maximization in social networks. Proceedings of the 15th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 199-208.

Examples

centrality_degree_discount(regulation_net)
#>    Explore       Plan    Monitor      Adapt    Reflect    Discuss Synthesize 
#>        0.9        0.8        1.0        0.7        0.6        0.3        0.4 
#>   Evaluate     Create      Share 
#>        0.2        0.5        0.1 
centrality_single_discount(regulation_net)
#>    Explore       Plan    Monitor      Adapt    Reflect    Discuss Synthesize 
#>        0.9        0.8        1.0        0.7        0.6        0.4        0.3 
#>   Evaluate     Create      Share 
#>        0.2        0.5        0.1