Computes, for each node, whether its strongest ties go to prominent nodes. The score is the mean weight of the node's ties to prominent neighbors divided by the mean weight of all its ties. A score above 1 means that the node's ties to prominent nodes are stronger than its average tie. A directed network is converted to an undirected one before the computation, with the weights of reciprocal edges summed, and self-loops are removed.
Usage
rich_club_local(
x,
prominence = NULL,
rich = c("k", "s"),
directed = NULL,
digits = NULL,
sort_by = "score",
...
)Arguments
- x
Network input: matrix, igraph, network, cograph_network, or tna object.
- prominence
Which nodes are prominent. Either a logical or 0/1 vector with one element per node (TRUE or 1 marks a prominent node), or a single number used as a threshold, in which case nodes with degree or strength strictly greater than it are prominent. If NULL (default), nodes with degree or strength strictly above the median are prominent.
- rich
Character.
"k"(degree, default) or"s"(strength). Used whenprominenceis NULL or a threshold.- directed
Logical or NULL. Default NULL (auto-detect).
- digits
Integer or NULL. Round scores. Default NULL.
- sort_by
Character or NULL. Column to sort by in descending order,
"score"(default) or"node". Any other value, and NULL, keep the node order.- ...
Passed to
to_igraph, which takes no further arguments, so any argument supplied here raises an error.
Value
A plain data frame with one row per node and columns node
(node label) and score. A node with no neighbors or no prominent
neighbor scores 1.
Details
For each node \(i\), \(r_i = \bar{w}_{i, rich} / \bar{w}_i\), where both means are taken over the ties of \(i\) with positive weight.
References
Opsahl, T., Colizza, V., Panzarasa, P. & Ramasco, J.J. (2008). Prominence and control: The weighted rich-club effect. Physical Review Letters, 101, 168702.