# Science Advances

## Supplementary Materials

**This PDF file includes:**

- section S1. Summarizing ICEWS

- section S2. Measuring influence using CCM

- section S3. Characterizing instances of reciprocity

- section S4. Varying thresholds for CCM reciprocity

- section S5. Country pairs with asymmetric influence

- fig. S1. The distributions of Goldstein scores by CAMEO event type occurring in
the ICEWS data set.

- fig. S2. The distribution of CAMEO quad classes in the ICEWS data set.

- fig. S3. The number of events per day during the entire ICEWS data set.

- fig. S4. Gaps in interactions between country pairs are small.

- fig. S5. An example from dynamical systems.

- fig. S6. Examples of shadow manifolds.

- fig. S7. Using nearest neighbors of shadow manifolds to recover variable

dynamics.

- fig. S8. Using CCM to infer causality between using United States (USA) treatment
of Saudi Arabia (SAU) and Saudi Arabia’s treatment of the United States (
*E*= 200, τ = 1).

- fig. S9. The number of pairs of countries exhibiting CCM reciprocity (
*y*axis) during four 5-year time periods (*x*axis) as we vary the minimum influence threshold (that is, minimum Pearson correlation of CCM reconstruction, indicated by color).

- fig. S10. CCM causation decreases with increased artificial noise.

- fig. S11. The effects of biased news data (λ = 0.00).

- fig. S12. The effects of biased news data (λ = 0.10).

- fig. S13. The effects of biased news data (λ = 0.20).

- fig. S14. The effects of biased news data (λ = 0.30).

- fig. S15. The effects of biased news data (λ = 0.40).

- fig. S16. The effects of biased news data (λ = 0.50).

- fig. S17. The effects of biased news data (λ = 0.60).

- fig. S18. The effects of biased news data (λ = 0.70).

- fig. S19. The effects of biased news data (λ = 0.80).

- fig. S20. The effects of biased news data (λ = 0.90).

- fig. S21 . Main results using CCM analysis with
*E*= 200 and τ = 2.

- fig. S22. Main results using CCM analysis with
*E*= 200 and τ = 3.

- fig. S23. Main results using CCM analysis with
*E*= 200 and τ = 4.

- fig. S24. Main results using CCM analysis with
*E*= 200 and τ = 5.

- fig. S25. Country pairs exhibiting CCM reciprocity are more likely to reciprocate
cooperation or conflict.

- fig. S26. The patterns of behavior in the day following an interaction.

- fig. S27. The patterns of behavior in the three days following an interaction.

- fig. S28. The patterns of behavior in the week following an interaction.

- fig. S29. The patterns of behavior in the month following an interaction.

- fig. S30. The effects of varying the CCM threshold for causality.

- fig. S31. Pairs of countries exhibiting CCM reciprocity that is, CCM(
*A, B*) ≥ 0.15 and CCM(*B, A*) ≥ 0.15 are connected using yellow edges.

- fig. S32. Pairs of countries exhibiting CCM reciprocity that is, CCM(
*A, B*) ≥ 0.15 and CCM(*B, A*) ≥ 0.20 are connected using yellow edges.

- fig. S33. Pairs of countries exhibiting CCM reciprocity that is, CCM(
*A, B*) ≥ 0.15 and CCM(*B, A*) ≥ 0.25 are connected using yellow edges.

- fig. S34. Pairs of countries exhibiting CCM reciprocity that is, CCM(
*A, B*) ≥ 0.15 and CCM(*B, A*) ≥ 0.30 are connected using yellow edges.

- fig. S35. Pairs of countries exhibiting CCM reciprocity that is, CCM(
*A, B*) ≥ 0.15 and CCM(*B, A*) ≥ 0.35 are connected using yellow edges.

- fig. S36. Pairs of countries exhibiting CCM reciprocity that is, CCM(
*A, B*) ≥ 0.15 and CCM(*B, A*) ≥ 0.40 are connected using yellow edges.

- fig. S37. Pairs of countries exhibiting CCM reciprocity that is, CCM(
*A, B*) ≥ 0.15 and CCM(*B, A*) ≥ 0.45 are connected using yellow edges.

- fig. S38. Pairs of countries exhibiting CCM reciprocity that is, CCM(
*A, B*) ≥ 0.15 and CCM(*B, A*) ≥ 0.50 are connected using yellow edges.

- table S1. Nations ordered by total imposed influence.

- table S2. The Pearson correlation for proportion of interactions of each quad class
between a pair of countries to the shared influence for that pair of countries.

- table S3. Country pairs ordered by increasing absolute difference in directed
influence that is, CCM(
*A, B*) − CCM(*B, A*).

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