weighted_kshell (Garas, Schweitzer & Havlin 2012)k-shell
decomposition on the generalized degree \(k' = (k^\alpha
s^\beta)^{1 / (\alpha + \beta)}\) (wks_alpha, wks_beta,
both 1), after the paper's weight normalization (divide by the mean,
then by the minimum, round to the nearest integer). Integer
thresholds label the shells, so unit weights give the k-core number
and isolates score 0. Reproduces the paper's Figure 1 example and its
Table 2 core size on the netscience network. Uses edge weights.
renewed_coreness (Liu, Tang, Zhou & Do 2015)Each link
gets the diffusion importance \(D_{ij} = (|N(j) \setminus N[i]| +
|N(i) \setminus N[j]|) / 2\); links below renewed_threshold
(paper: 2) are removed and the k-core number of the residual graph is
the renewed coreness. A clique with no outside links collapses to 0.
Reproduces the paper's Figure 1 and all twelve percentages of its
supplementary Table S1; the Zoo's transcription with open
neighborhoods is off by one.
geodesic_kpath (Borgatti & Everett 2006)The number of
shortest paths of length at most kpath_k (default 3) that
start at the node, counted with multiplicity. Note that
centiserve::geokpath counts nodes within \(k\) instead,
which is the paper's vertex-disjoint variant and equals m-reach.
geodesic_kpath follows mode; the other two ignore
direction.
centrality_weighted_kshell(x, wks_alpha = 1, wks_beta = 1, ...)centrality_renewed_coreness(x, renewed_threshold = 2, ...)
centrality_geodesic_kpath(x, mode = "all", kpath_k = 3, ...)
Named numeric vector, one value per node.
Network input (matrix, igraph, network, cograph_network, tna object).
Exponents of degree and strength in the weighted k-shell. Default 1 and 1.
Additional arguments passed to centrality.
Diffusion-importance threshold. Default 2.
For directed networks: "all" (default), "out"
(distances along out-edges), or "in".
Maximum path length. Default 3.
Garas, A., Schweitzer, F., & Havlin, S. (2012). A k-shell decomposition method for weighted networks. New Journal of Physics, 14, 083030.
Liu, Y., Tang, M., Zhou, T., & Do, Y. (2015). Improving the accuracy of the k-shell method by removing redundant links: From a perspective of spreading dynamics. Scientific Reports, 5, 13172. tools:::Rd_expr_doi("10.1038/srep13172").
Borgatti, S. P., & Everett, M. G. (2006). A graph-theoretic perspective on centrality. Social Networks, 28(4), 466-484.
centrality_coreness, centrality_s_shell,
centrality_kreach.
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_weighted_kshell(adj)
centrality_renewed_coreness(adj)
centrality_geodesic_kpath(adj, kpath_k = 2)
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