Five node measures that other centrality packages expose and
centrality() did not. Each is a thin wrapper on
centrality.
centrality_local_efficiency(x, mode = "all", ...)centrality_s_core(x, ...)
centrality_fragmentation(x, mode = "all", ...)
centrality_kpath(x, mode = "all", kpath_len = 3, ...)
centrality_epc(x, epc_threshold = 0.5, epc_runs = 1000, epc_seed = NULL, ...)
Named numeric vector, one value per node.
Network input: matrix, igraph, network, cograph_network, or tna object.
Direction: "all", "out" or "in".
Additional arguments passed to centrality.
Maximum path length for centrality_kpath.
Default 3.
Edge removal probability. Default 0.5.
Number of percolation realizations. Default 1000.
Random seed. Default NULL, which leaves the
caller's stream alone and makes the estimate vary between calls.
local_efficiency (Latora & Marchiori 2001)The global
efficiency of the subgraph induced on the node's neighbors, the node
itself removed: the mean of \(1 / d_{jl}\) over ordered pairs of
neighbors, with distances measured inside that subgraph. Nodes with
fewer than two neighbors score 0. High values mark a node whose
neighborhood survives its loss. Matches
igraph::local_efficiency() and
brainGraph::efficiency(type = "local").
s_core (Eidsaa & Almaas 2013)The weighted k-core: the largest strength threshold \(s\) whose maximal subgraph of nodes with strength at least \(s\) still contains the node. Unit weights give the k-core number exactly. Uses edge weights.
fragmentation (Borgatti 2006)Distance-weighted
fragmentation of the network after deleting the node: \(1 - \sum
1/d_{ij} / ((n-1)(n-2))\) over the ordered pairs that remain. Higher
means a more disruptive removal. Matches
keyplayer::fragment() on unweighted input.
kpath (Sade 1989)The number of simple paths of length at
most kpath_len (default 3) that the node lies on, endpoints
included; length 1 alone reproduces degree. Matches the per-vertex
column sums of sna::kpath.census(). Enumeration is exhaustive,
so cost grows with branching factor to the power kpath_len.
epc (Lin et al. 2008)Edge percolated component: each
edge survives with probability 1 - epc_threshold, and the
score is the mean size of the node's component over epc_runs
realizations, as a share of the network. cytoHubba and
centiserve::epc() divide by the node count alone, so their
number is epc_runs times this one; the ranking is the same.
A Monte Carlo estimate -- pass epc_seed for a reproducible
value.
local_efficiency, fragmentation and kpath follow
mode; s_core and epc read the undirected skeleton.
Latora, V., & Marchiori, M. (2001). Efficient behavior of small-world networks. Physical Review Letters, 87(19), 198701.
Eidsaa, M., & Almaas, E. (2013). s-core network decomposition: A generalization of k-core analysis to weighted networks. Physical Review E, 88(6), 062819. tools:::Rd_expr_doi("10.1103/PhysRevE.88.062819").
Borgatti, S. P. (2006). Identifying sets of key players in a social network. Computational and Mathematical Organization Theory, 12(1), 21-34.
Sade, D. S. (1989). Sociometrics of Macaca mulatta III: n-path centrality in grooming networks. Social Networks, 11(3), 273-292.
Lin, C.-Y., Chin, C.-H., Wu, H.-H., Chen, S.-H., Ho, C.-W., & Ko, M.-T. (2008). Hubba: hub objects analyzer, a framework of interactome hubs identification for network biology. Nucleic Acids Research, 36, W438-W443. tools:::Rd_expr_doi("10.1093/nar/gkn257").
centrality_coreness,
centrality_weighted_kshell,
centrality_geodesic_kpath,
network_local_efficiency.
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_local_efficiency(adj)
centrality_s_core(adj)
centrality_fragmentation(adj)
centrality_kpath(adj, kpath_len = 2)
centrality_epc(adj, epc_runs = 50, epc_seed = 1)
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