Maximal clique centrality

For every maximal clique C containing a vertex, add \((|C|-1)!\). Only maximal cliques count: a clique contained in a larger clique is excluded. This is Chin et al.'s MCC, not a count of all cliques.

Usage

centrality_mcc(x, ...)

Arguments

x: Network input accepted by centrality.
...: Additional arguments to centrality. With normalized = TRUE, positive scores are divided by their maximum.

Value

Named numeric vector in input node order.

Details

Uses the simple undirected, unweighted skeleton: either direction creates an edge, parallel edges count once, and self-loops are removed. Singleton cliques are excluded, so isolates score zero. This is an explicit cograph convention consistent with the paper's degree reduction when neighbors have no edges between them. Reading the printed sum literally with singleton cliques would instead assign isolates \(0! = 1\).

Maximal clique enumeration has exponential worst-case cost. MCC is held back from centrality(type = "all"); select it explicitly or use include = "mcc". Scores use double precision; overflow raises an error, including any clique with more than 171 vertices. Normalization happens after raw calculation and does not bypass this limit.

References

Chin, C. H., et al. (2014). cytoHubba: identifying hub objects and sub-networks from complex interactome. BMC Systems Biology, 8(Suppl 4), S11. doi:10.1186/1752-0509-8-S4-S11 .

Examples

centrality_mcc(igraph::make_full_graph(5))
#>  1  2  3  4  5 
#> 24 24 24 24 24