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 \(1 / n\).
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.
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.