NCVoteRank

NCVoteRank (Kumar and Panda 2020) is VoteRank (Zhang et al. 2016) with the voting ability of each voter weighted by its neighborhood coreness. A node collects the score $$s_u = \sum_{v \in N(u)} va_v \,[\theta + (1 - \theta)\, nc_v], \qquad nc_v = \frac{\sum_{w \in N(v)} ks(w)}{\max_j \sum_{w \in N(j)} ks(w)},$$ with $ks$ the k-shell index. The top scorer is elected, its ability drops to 0, its neighbors lose $1/\langle k \rangle$ and the nodes two steps away lose $1/(2\langle k \rangle)$.

Usage

centrality_ncvoterank(x, ncvote_theta = 0.5, ...)

Arguments

x: Network input accepted by centrality.
ncvote_theta: Weight $\theta$ of the plain vote (default 0.5).
...: Further arguments to centrality, such as normalized.

Value

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

Details

The measure is computed on the simple undirected skeleton of the network, so direction, weights and loops are ignored. Elections continue until every node is placed. The first elected scores 1 and the last $1/n$, so scores lie in $(0, 1]$. The definition follows the Centrality Zoo and three independent restatements of the article, and the scaling of the coreness by its maximum follows Yu et al. (2020). With $\theta = 1$ and no two-step weakening the procedure is VoteRank.

References

Kumar, S., & Panda, B. S. (2020). Identifying influential nodes in social networks: Neighborhood coreness based voting approach. Physica A, 553, 124215.

Zhang, J.-X., Chen, D.-B., Dong, Q., & Zhao, Z.-D. (2016). Identifying a set of influential spreaders in complex networks. Scientific Reports, 6, 27823.

Examples

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