Congestion centrality ρ_{max} as a function of the network parameters (*m*, λ, ζ). For both plots, the underlying hierarchy of the networks examined here has *N* = 3905 nodes with branching ratio *b* = 5 and depth *L* = 6. (*A*) Contour plot of ρ_{max}(λ, ζ) for ξ = 1 averaged over an ensemble of 100 networks. Lighter regions correspond to lower values of ρ_{max}(λ, ζ). For each parameter pair (λ, ζ), *m* = *N* links are added and the resulting network is tested by initiating messages at each node with probability μ = 2.561 × 10^{-3} for *T* = 10^{3} time steps (i.e., an average of 10 messages are generated per time step). The broad local minimum centered around (λ, ζ) = (0.5, 0.5) corresponds to multiscale networks. (*B*) Change in ρ_{max} with the addition of links. The networks tested here are random (λ = ∞, ζ = ∞, ▿, local team (λ = ∞, ζ = 0, ⋄), random interdivisional (λ = 0, ζ = ∞, ▵), core-periphery (λ = 0.1, ζ = 0.15, ○), and multiscale (λ = 0.5, ζ = 0.5, □). Each data point is the average of 100 realizations. In the case of multiscale networks, most of the reduction of ρ_{max} is obtained by the addition of only *m* = *N* links (the same holds for <ρ>).

## PubMed Commons