Density of Maximum Neighborhood Component (DMNC)

Edges divided by nodes raised to dmnc_epsilon, both taken from the largest connected component of the subgraph induced on a node's neighbors (the focal node excluded).

Usage

centrality_dmnc(x, mode = "all", dmnc_epsilon = 1.7, ...)

Arguments

x

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

mode

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

dmnc_epsilon

Numeric. Epsilon exponent for DMNC. Default 1.7 as recommended by Lin et al. (2008). centiserve uses 1.67 (four-community assumption). Must be between 1 and 2.

...

Additional arguments passed to centrality (e.g., normalized, weighted, directed).

Value

Named numeric vector of DMNC values.

Divergence from centiserve

centiserve::dmnc() returns different values, and not only because of its different epsilon default. Its edge count is taken with induced.subgraph(graph, which(c$membership %in% ...)), where the membership vector indexes the neighborhood subgraph but is used to subset the original graph. The two index spaces are not the same, so the edges counted are those of an unrelated vertex set. On the Zachary karate club the two disagree on 14 of 34 nodes at a matched epsilon, and reproducing that indexing exactly reproduces centiserve's output. cograph counts the edges of the component it actually found.

See also

centrality for computing multiple measures at once, centrality_mnc for the size-only variant.

Examples

adj <- matrix(c(0, 1, 1, 1, 0, 1, 1, 1, 0), 3, 3)
rownames(adj) <- colnames(adj) <- c("A", "B", "C")
centrality_dmnc(adj)
#>         A         B         C 
#> 0.3077861 0.3077861 0.3077861