Community Hub-Bridge Centrality

Community hub-bridge centrality (Ghalmane, El Hassouni and Cherifi 2019) scores nodes that are 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 size of the community of $i$, $k^{intra}_i$ and $k^{inter}_i$ its numbers of links inside and outside that community, and $NNC_i$ the number of other communities it links to.

Usage

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

Arguments

x: Network input accepted by centrality.
membership: Community labels, one per node, for example from detect_communities.
mode: For directed networks: "all" (default), "out" or "in".
...: Further arguments to centrality, such as normalized.

Value

A named numeric vector with one score per node, in input node order.

Details

Edge weights and self-loops are ignored. Under mode = "out" or mode = "in" only out-links or in-links count, and the default ignores direction. This is the raw form of the original article. Later work by the same group uses a normalized variant with the same name. Without membership the function raises a warning of classes cograph_bad_membership and cograph_undefined_measure and returns NA for every node. A membership that is not one non-missing label per node raises an error of class cograph_bad_membership.

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

centrality_community_hub_bridge(regulation_net,
                                membership = rep(1:2, each = 5))
#>    Explore       Plan    Monitor      Adapt    Reflect    Discuss Synthesize 
#>         13         10         19         14         13          9          4 
#>   Evaluate     Create      Share 
#>          9         18          9