Community Hub-Bridge Centrality

Ghalmane, El Hassouni and Cherifi's (2019) score for nodes that are both hubs inside their community and bridges between communities: $$CHB(i) = |C_i| \, k^{intra}_i + NNC_i \, k^{inter}_i,$$ where $|C_i|$ is the number of nodes in $i$'s own community, $k^{intra}_i$ and $k^{inter}_i$ its numbers of links inside and outside that community, and $NNC_i$ the number of other communities it is linked to (eqs. 2 to 4 of the paper). Higher values mark nodes whose removal both fragments their community and cuts links between communities. A normalized variant with the same name exists in later work by the same group; this is the original raw form.

Usage

centrality_community_hub_bridge(x, membership = NULL, mode = "all", ...)

Arguments

x: Network input (matrix, igraph, network, cograph_network, tna object).
membership: Community labels, one per node. Required; without it the function warns and returns NA. Obtain one from detect_communities.
mode: For directed networks: "all" (default), "out", or "in".
...: Additional arguments passed to centrality.

Value

Named numeric vector, one value per node.

Details

Under mode = "out" or "in" only out- or in-links count; the default ignores direction. Edge weights are ignored.

Conditions

Raises an error of class cograph_bad_membership when membership is not one non-missing label per node.

References

Ghalmane, Z., El Hassouni, M., & Cherifi, H. (2019). Immunization of networks with non-overlapping community structure. Social Network Analysis and Mining, 9, 45.

Examples

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_community_hub_bridge(adj, membership = c(1, 1, 1, 2, 2, 2))
#> A B C D E F 
#> 6 6 7 7 6 6