centrality_ncvoterank: NCVoteRank

In cograph: Analysis and Visualization of Complex Networks

NCVoteRank

Description

Kumar and Panda's (2020) neighborhood-coreness VoteRank. As in VoteRank, every node votes for its neighbors with its voting ability, the top scorer is elected, and the abilities around it are weakened; here each voter's ability is additionally weighted by its neighborhood coreness,

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 (Bae & Kim 2014) and \theta = 0.5. After an election the winner's ability drops to 0, its neighbors lose 1 / \langle k \rangle and the nodes two steps away lose 1 / (2 \langle k \rangle). Elections continue until every node is placed, as in centrality_voterank; the first elected scores 1, the last 1 / n.

Usage

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

Arguments

x	Network input (matrix, igraph, network, cograph_network, tna object).
ncvote_theta	Weight \theta of the plain vote. Default 0.5.
...	Additional arguments passed to centrality.

Details

Provenance. The original Physica A article could not be obtained; this definition follows the Centrality Zoo encyclopedia (Shvydun 2025) and three independent restatements (Yu et al. 2020, Li et al. 2022, Zhu et al. 2023), which agree on the voter-side coreness weighting. The scaling of the coreness term by its maximum follows Yu et al., who state the coreness is normalized without giving the form. With \theta = 1 and no two-hop weakening the procedure is exactly VoteRank, which is reproduced against networkx.voterank. Defined for undirected graphs; direction, weights and loops are ignored.

Value

Named numeric vector in (0, 1], one score per node.

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.

See Also

centrality_voterank.

Examples

adj <- matrix(0, 6, 6)
adj[cbind(c(1, 1, 2, 4, 4, 5, 3), c(2, 3, 3, 5, 6, 6, 4))] <- 1
adj <- adj + t(adj)
rownames(adj) <- colnames(adj) <- LETTERS[1:6]
centrality_ncvoterank(adj)

cograph documentation built on Sept. 30, 2026, 5:08 p.m.