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Global Reaching Centrality (Mones, Vicsek & Vicsek 2012)

Source: R/centrality.R
reaching_global.Rd

A graph-level hierarchy measure computed from per-node local reaching centralities: $$GRC(G) = \frac{1}{N - 1} \sum_v \left( \max_u LRC(u) - LRC(v) \right)$$

Usage

reaching_global(x, mode = "all", ...)

Arguments

x

Network input (matrix, igraph, network, cograph_network, tna object).

mode

For directed networks: "all" (default), "in", or "out".

...

Additional arguments passed to centrality_reaching_local.

Value

A single numeric value in \([0, 1]\).

Details

Values close to 0 indicate a flat network (all nodes reach equal proportions of the graph); values close to 1 indicate strong hierarchical structure. Matches networkx.global_reaching_centrality exactly.

References

Mones, E., Vicsek, L., & Vicsek, T. (2012). Hierarchy measure for complex networks. PLoS ONE, 7(3), e33799.

See also

centrality_reaching_local, summarize_network.

Examples

# Star graph: highly hierarchical (directed out from center)
adj <- matrix(0, 5, 5)
adj[1, 2:5] <- 1
rownames(adj) <- colnames(adj) <- LETTERS[1:5]
reaching_global(adj, mode = "out")
#> [1] 1