Fig 1.
Rich-club coefficients in IPv4 and IPv6 Networks.
(a) and (b) show the rich-club coefficients for the top-n (n = 10,30,50) highest-degree nodes in the IPv4 and IPv6 networks, respectively, from 2015 to 2024.
Fig 2.
Cooperation pattern within individual countries/regions.
(a) and (b) show the median assortativity coefficients (r) and the corresponding full (0% − 100%) and interquartile (25% − 75%) ranges for country/region-level sub-networks (consisting of ASes with identical country/region labels) in IPv4 and IPv6 networks at each time snapshot. (c) and (d) present the median NODF values and corresponding percentile ranges for the same set of sub-networks in IPv4 and IPv6 networks at each time snapshot, respectively. Circles or squares in the panels represent the assortativity or NODF value of the global network without country/region partitioning.
Fig 3.
Cooperation among countries/regions.
Relationship between modularity Q and average degree in IPv4 and IPv6 networks. Each dot corresponds to a snapshot of the network, with its color indicating the corresponding time. Results for IPv4 and IPv6 networks are highlighted with blue and red shading, respectively.
Fig 4.
Number of edges in TOP20 countries/regions.
Variations in the number of intra- and inter-edges for countries/regions over the entire 120-month period in (a) IPv4 and (b) IPv6 networks. Countries/regions are sorted by their contributions to the total number of edges in the respective networks, and the top 20 are presented.
Fig 5.
Visualization of cooperation tendency.
Visualization of international cooperation tendencies for countries/regions in (a) IPv4 and (b) IPv6 networks. Each shaded area with labels reflects the changes in the number of total edges and the proportion of inter-edges of that country/region over the past decade. Dots within each shadow indicate the specific values at each time snapshot.
Fig 6.
Visualization of Geopolitical Events Impact.
Case studies on the impact of geopolitical events on international cooperation for the countries/regions involved. (a) and (b) show how the top five countries/regions with which Ukraine and the Taiwan region of China most frequently cooperated in terms of AS-level connections changed before and after the respective events. The month in which each event occured is highlighted with red shading.