Fig. 3. Conflict onset by degree of separation for geographically contiguous states in the alliance network.

Pairs of states that are not connected at any degree are denoted as infinite (“Inf”), and conflict onsets are observed between contiguous states at up to five degrees of separation. (Left) Rate of conflict onset from the raw data, with the pink horizontal line indicating the average rate for contiguous dyads. The first three degrees of separation see below-average conflict onset rates. (Right) Dyads at degrees of separation ranging from one to four are sampled, and their respective conflict probabilities conditional on the rest of the network are computed. The plot shows the probability of conflict when an alliance is present or absent between a contiguous pair of states with 95% confidence intervals. The probability of conflict drops substantially between contiguous states indirectly allied up to three degrees.