Fig 1.
Probability density function fϕ(x) of the vulnerability ϕ of an airport.
The average vulnerability is E[ϕ] = 0.15 and the variance is Var[ϕ] = 0.01. In total 45 bins are split within the interval [0, 1] with the same bin size. The probability density fϕ(x) at a given bin x eqals the percentage of the airports whose vulnerability falls within the bin normalized by the bin size 1/45.
Fig 2.
The probability density functions of the weight
of a link (a) and fS(x) of the strength S of a node (b) in network G2 (blue points) and G3 (red points).
Horizontal and vertical axes are presented in logarithmic scale. The horizontal axis is split into 20 bins, each with the same bin size in the linear scale. The probability density (fS(x)) at a given bin x is equal to the fraction of the links (nodes) whose weight (strength) falls within the bin normalized by the bin size. Both link weight and node strength have, respectively, a higher average in G3 and higher coefficient of variation (the ratio of standard deviation over the average) in G2.
Table 1.
The linear correlation coefficient of node strength with clustering coefficient, betweenness, closeness and eigenvector centrality respectively in network G1, G2 and G3.
Fig 3.
Airport vulnerability versus a nodal centrality metric.
The scatter plot of airport vulnerability ϕ versus node strength (a,b,c), clustering coefficient (d,e,f), betweenness (g,h,i), closeness (j,k,l) and eigenvector (m,n,o) centrality in network G1 (first column, blue color), G2 (second column, red color) and G3 respectively.
Fig 4.
Geographic location and vulnerability of U.S. airports.
The geographic location and vulnerability of an airport in U.S. mainland (a), Alaska (b), Hawaii Islands (c), Puerto Rico (d), American Samoa and Guam (e). The nodes/airports are color-coded according to their airport vulnerability ϕ. We show the names of the top 30 most vulnerable airports.
Fig 5.
The scatter plot of the recognition quality ξ versus Jansen-Shannon divergence JSD for both heterogeneous and homogeneous SIS model with diverse parameter sets.
The scatter plot is obtained in network G1 (figure a1, a2), G2 (b1, b2) and G3 (c1, c2). Points correspond to the heterogeneous model, where θ ∈ [0, 2] with step size 0.1 and c ∈ (0, 2] with step size 0.02. The points are colored according to parameter c in a1, b1, c1 and according to θ in a2, b2, c2. The dash lines correspond to the baseline homogeneous model.
Fig 6.
Airport vulnerability and nodal infection probability versus normalized node strength.
The scatter plot of the vulnerability ϕ (points) and infection probability v (lines) of a node versus the normalized node strength of the node on the underlying network topology G1. The black dashed line corresponds to the baseline homogeneous model (θ = 0). Solid lines correspond to the heterogeneous model with θ = 1.50, colored according to the parameter c (figure a) or with c = 0.02, colored according to the parameter θ (figure b).
Fig 7.
Cumulative distribution of in each network when θ = 1.5.