Risky cascading transitions in international relationships

Abstract

Changing attitudes in diplomatic relations is a common feature of international politics. However, such changes may trigger risky domino-like cascades of "friend-to-enemy" transitions among other counties and yielding catastrophic damage that could reshape the global network of international relationships. While previous attention has been focused on studying single pairs of international relationships, due to the lack of a systematic framework, it remains still unknown whether, and how, a single transition of attitude between two countries could trigger a cascade of attitude transitions among other countries. Here, we develop such a framework and construct a global evolving network of relations between country pairs based on 70,756,728 international events between 1,225 country pairs from January 1995 to March 2020. Our framework can identify and quantify the cascade of transitions following a given original transition. Surprisingly, weaker transitions are found to initiate most of the largest cascades. We also find that transitions are not only related to the balance of the local environment, but also global network properties such as betweenness centrality. Our results suggest that these transitions have a substantial impact on bilateral trade volumes and scientific collaborations. Our results reveal reaction chains of international relations, which could be helpful for designing early warning signals and mitigation methods for global international conflicts.

Keywords: Cascade effects; Complex system; Computational framework; International relationships.

Fig. 1.

Demonstration of the country relations network and transitions. Demonstration of (a) individual pair of country relations; (b) its local environment; and (c) network environment. (d) Demonstration of the country relations networks for two months: February 2011 (left), March 2011 (right). Link width represents the average score (Goldstein) of a pair relations in a given month, where links of Syria and Israel to other countries are highlighted for visualization. Orange links represent negative relations and green exhibits positive relations. (e) The average Goldstein time series between Israel and Syria during the last 25 years. Green and orange points exhibit positive (denoted by ) and negative relations (denoted by ), respectively. The strength of a transition, , is demonstrated in the inset and is calculated according to Eq. (1), in which n equals 24 months (see Fig. S1 in SI Appendix for robustness analysis). If there are no transitions, strength is assumed to be 0. (f) Distributions of all transition strength on a semi-log scale. The straight line suggests exponential distribution with a typical strength close to 0.2. Moreover, approximately 20% PN and NP transitions are greater than 0.25, which are regarded as strong transitions in this paper. (see Fig. S3 in SI Appendix for more statistical results of transitions). (g) Time-line of the five strongest PN transitions and five strongest NP transitions in the world during the last 25 years (see Table S1 in SI Appendix for country name and corresponding code).

Fig. 2.

Spatio-temporal correlations between transitions. (a) We measure the relative network distance between different PN (NP) transitions that happens in the same month [see also Fig. S5(a) in SI Appendix]. The x-axis is the strength threshold of transition. Only transitions with strength above this threshold are considered. The y-axis is the relative network distance, defined as (D−D_r)/D_r, where D is the distance between the two country pairs in the real network and D_r is the average distance in a corresponding random network (see details in SI Appendix). (b) and (c) The x-axis is the strength threshold. For each specific (b) PN or (c) NP transition, we measure the average strength of its D = 1 nearest neighboring transitions (circles) and D ≥ 2 further neighboring transitions (triangles) in the same month as the y-axis. (d) The relative time intervals between successive PN (NP) transitions of the same country pair are measured [see also Fig. S5(b) in SI Appendix]. The x-axis is the strength threshold. The y-axis is the relative time interval of each two successive transitions of the same country pair, which is defined as (l−l_r)/l_r. Here, l is the real time interval and l_r is the time interval in a controlled random time series (see Fig. S6 in SI Appendix for significant test). (e) and (f) τ is a time window, which is used to measure the transitions within (t, t+τ). The x-axis is the strength threshold. For each specific (e) PN or (f) NP transition, we measure the average strength of its transitions (circles) of the same country pair within (t, t+τ) and within (t+τ, 302) as the y-axis. Here, we chose τ to be 12 months (see Fig. S7 in SI Appendix for other parameters analysis).

Fig. 3.

Cascading transitions. To demonstrate the cascading transition in the country network, we show (a) one PN transition and (b) one NP transition as the starting events of the cascade and plot their resulting cascades. These two transitions represent the Syria–Israel conflict in 2011 and the easing hostility between United States and Iraq in 2007, respectively. In the tree-like figures, PN transitions are shown as red lines and NP transitions are shown as blue lines. In (c) and (d), the x-axis is the spanning month after the seed transitions. The y-axis is (c) the number of new transitions in this month and (d) the maximal strength of new transitions in this month. A box chart is constructed of a set of whiskers and a box, which is drawn from the first quartile to the third quartile with a horizontal line to represent the median.

Fig. 4.

Statistics of cascading transitions. In (a) to (d), the x-axis is the strength of seed transitions. The y-axis is (a) the size of cascades (number of country pairs), (b) the cascading speed (ratio between number of country pairs and spanning months), (c) the average strength of all the following PN and NP transitions, (d) the fraction of the same type transitions with respect to all transitions in the cascades. (e) The distributions of seed transition strength for top 10% largest cascades and other cascades. Top 10% largest cascades are ranked by the number of country pairs in the cascades.

Fig. 5.

Network properties of transitions. (a) Green (red) circles represent the transition probability P(PP) [P(PN)], which is the fraction of positive (negative) relations in t + 1 out of positive relations in month t, when considering all country pairs and all months. Blue (orange) circles represent the transition probability P(NP) [P(NN)], which is the fraction of positive (negative) relations in month t + 1 out of the negative relations in month t. Plus signs represent the randomized probabilities. The betweenness centrality is normalized between [0,1] by max–min method. (b) Higher betweenness centrality links have on average higher transition strength. (c) Demonstration of the betweenness centrality of links and the eight possible balanced configurations as well as unbalanced structures with respect to an AC pair. As demonstrated, the betweenness centrality of a link in a monthly network is measured here by the average betweenness centrality of the nodes at both ends (see Fig. S11 for the difference between the defined betweenness and traditional link betweenness). The nodes are countries and the links are the relationships among countries. In order to reflect the link centrality from structural level, betweenness centrality is set unweighted and unsigned. The balanced ratio of a link is defined as the number of balanced triangles divided by all triangles for each month. Green and orange links exhibit positive and negative relations, respectively. (d) The x-axis is the balanced ratio of a link in a given month. The symbols have the same meaning as (a). (e) shows that highest strength emerges from links whose balanced ratio is around 0.5.

Fig. 6.

Relationship between transitions and bilateral trade volume, as well as joint scientific papers. For a country pair, the x-axis is the pair transition fraction, calculated by the number of transitions (number of NP,PN), this pair had divided by the sum of all possible states (number of PP,PN,NP,NN). The y-axis is (a) fraction of joint scientific papers between a country pair and (b) the fraction of bilateral trade volume between a country pair (see SI for more details). Inset figures show the Pearson cross correlation of each scatter plot. The x-axis is the shifting steps and the y-axis is the Pearson correlation value. The shifting shows the level of noise in the data, which is significantly smaller than the signal (Pearson correlations) at shifting = 0. (c) The x-axis is the largest fraction of transitions within a 3-years period for each country pair (see SI for more details). The y-axis is the fraction of transitions in the rest of the corresponding time. The pink circles represent country pairs with relatively large difference of transition between most transition period and the rest of time. These country pairs are utilized to calculate results in (d) and (e). The grey circles are not considered in the following results. (d) The x-axis is the normalized fraction of papers in the time period of 3 years with most transitions. The y-axis is the normalized fraction of papers in the rest of the time. (e) The x-axis is the normalized trade in the time period of 3 years with most transitions. The y-axis is the normalized trade in the rest time.