Figure 2.

The impact of mobility on geographical collaboration networks. C⁺ ∩ c⁻_i(C⁻ ∩ c⁺_i) represents the geographical overlap between a researcher's location before (after) migrating, denoted by c⁻_i(c⁺_i), and the set of collaborator locations after (before) migrating, denoted by C⁺(C⁻). (a) Shown is the fraction of mobility events corresponding to: (i) ‘blind mobility’ (blue): in which there is no overlap between a researcher's prior location and the locations of future collaborators (f[C⁺ ∩ c⁻_i = 0] = 0.34); and (ii) ‘curtail mobility’ (red): in which there is no overlap between the locations of a researcher's prior collaborators and his/her destination country (f[C⁻ ∩ c⁺_i = 0] = 0.11). (b) The distributions of collaboration network integrity, measured by f[C⁺ ∩ c⁻_i] and f[C⁻ ∩ c⁺_i], are right-skewed: on average there is only a 16% overlap between C⁺ and c⁻_i and a 23% overlap between C⁻ and c⁺_i. (c) The difference Δ[C ∩ C] measures the change in the amount of geographical overlap (see equation (2.2)), measured in two ways: per affiliation and per country. Negative values indicate more overlap before as compared to after. Both methods indicate relatively high levels of collaboration network disintegration following a mobility event: 89% (70%) of the values are negative when measuring per affiliation (per country). Shown are calculations on data aggregated across all three periods, T₁₂₃; for analogous plots specific to a given period T see electronic supplementary material, figure S6. Vertical lines indicate distribution mean values. (Online version in colour.)