Hubbell Centrality

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, ...)

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.

Value

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

Details

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

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.

References

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

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)
#>        A        B        C        D 
#> 1.208459 1.389728 1.389728 1.208459