cograph (version 2.7.2)

centrality_hubbell: Hubbell Centrality

Description

Hubbell (1965) input-output centrality: \(C = (I - w W)^{-1} \mathbf{1}\), where \(W\) is the (weighted) adjacency matrix and \(w\) is a weight factor that must satisfy \(w \cdot \rho(W) < 1\) for the system to be solvable.

Usage

centrality_hubbell(x, hubbell_weight = 0.5, ...)

Value

Named numeric vector of Hubbell centrality values (or NA if the system is not solvable).

Arguments

x

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

hubbell_weight

Attenuation factor \(w\). Default 0.5. If \(w \cdot \rho(W) \ge 1\), the function returns NA with a warning.

...

Additional arguments passed to centrality.

Note on centiserve equivalence

centiserve::hubbell(g, weights = NULL) silently resets all edge weights to 1, ignoring the graph's weight attribute. To reproduce cograph's values with centiserve on a weighted graph, pass weights = igraph::E(g)$weight explicitly.

Details

Bit-exact match against centiserve::hubbell when edge weights are passed explicitly (cograph mirrors centiserve's full-inverse LAPACK call path).

References

Hubbell, C. H. (1965). An input-output approach to clique identification. Sociometry, 28(4), 377-399.

See Also

centrality, centrality_katz.

Examples

# Small weighted path graph; spectral radius permits weightfactor = 0.5
adj <- matrix(0, 4, 4)
adj[1,2] <- adj[2,1] <- adj[2,3] <- adj[3,2] <- adj[3,4] <- adj[4,3] <- 0.3
rownames(adj) <- colnames(adj) <- LETTERS[1:4]
centrality_hubbell(adj, hubbell_weight = 0.5)