A graph-level hierarchy measure computed from per-node local reaching centralities: $$GRC(G) = \frac{1}{N - 1} \sum_v \left( \max_u LRC(u) - LRC(v) \right)$$
Arguments
- x
Network input (matrix, edge-list data frame, igraph, network, cograph_network, tna object).
- mode
For directed networks:
"all"(default),"in", or"out".- ...
Additional arguments passed to
centrality_reaching_local.
Value
A single numeric value. On an unweighted graph it lies in \([0, 1]\). On a weighted graph the local reaching centralities scale with the edge weights, so the value is unbounded. A graph with at most one node returns 0.
Details
Values close to 0 indicate a flat network in which all nodes reach equal
proportions of the graph. Larger values indicate a more hierarchical
structure. The result matches networkx.global_reaching_centrality.
References
Mones, E., Vicsek, L., & Vicsek, T. (2012). Hierarchy measure for complex networks. PLoS ONE, 7(3), e33799.