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Additional file 1. Supplementary information regarding precise definitions of static centralities (Section S1), variance in the simulated outbreak sizes (Section S2), the relative weight of markets and assembly centres in highly ranked nodes (Section S3), the impact of using different yearly datasets to compute centralities (Section S4), the impact of varying epidemic parameters (Section S5), and the impact of varying random walk parameters to approximate TempoRank measures (Section S6).

We give an explicit construction of the increasing tree-valued process introduced by Abraham and Delmas using a random point process of trees and a grafting procedure. This random point process will be used in companion papers to study record processes on L��vy trees. We use the Poissonian structure of the jumps of the increasing tree-valued process to describe its behavior at the first time the tree grows higher than a given height. We also give the joint distribution of this exit time and the ascension time which corresponds to the first infinite jump of the tree-valued process.