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Figure 1.

Nodes and links of the network.

(left) Nodes of the network. Each node graphically coincides with the center of an active spatial cell. Red symbols correspond to the nodes of the network () with the additional physical constraint, km, while blue symbols correspond to the nodes of the network () without this constraint. (right) Number of links, , as a function of the physical distance, [ km]. The scale of values is in km, the red line indicates the physical threshold, km.

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Figure 1 Expand

Figure 2.

Degree centrality,

. Large values correspond to highly connected nodes.

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Figure 2 Expand

Figure 3.

Exceedance probability of the node degree,

.

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Figure 3 Expand

Figure 4.

Weighted average topological distance and average physical distance.

(top) Weighted average topological distance, . The scale of values spans in the interval [6], [12]. Higher values are reported without distinction with grey color. (bottom) Average physical distance, . The scale of values is in km.

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Figure 4 Expand

Figure 5.

Long-range network,

km. (left) Degree centrality. (right) Weighted average topological distance. The scale of values spans in the interval [8], [16], while higher values are reported without distinction with grey color.

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Figure 6.

Local clustering and betweenness centrality measures.

(top): local clustering coefficient, . (middle): Probability density function, , of the local clustering coefficient, C. The red line represents the global clustering coefficient, . (bottom): betweenness centrality ( plot is shown).

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Figure 6 Expand

Figure 7.

Shortest path,

, of 4 significant nodes of the network. The measured nodes are represented in each panel by a pink square. (A) Northern Europe, node coordinates: ( E, N). (B) Southern Europe, node coordinates: ( E, N). (C) South America, node coordinates: ( W, S). (D) Asia, node coordinates: ( E, N).

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Figure 7 Expand

Figure 8.

Physical area connected to a node as a function of the topological distance,

. The four nodes of Fig. 7 are displayed.

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Figure 8 Expand