Navigability evaluation of complex networks by greedy routing efficiency

Abstract: Network navigability is a key feature of complex networked systems. For a network embedded in a geometrical space, maximization of greedy routing (GR) measures based on the node geometrical coordinates can ensure efficient greedy navigability. In PNAS, Seguin et al. (PNAS 2018, vol. 115, no. 24) define a measure for quantifying the efficiency of brain network navigability in the Euclidean space, referred to as the efficiency ratio, whose formula exactly coincides with the GR-score (GR-efficiency) previously published by Muscoloni et al. (Nature Communications 2017, vol. 8, no. 1615). In this Letter, we point out potential flaws in the study of Seguin et al. regarding the discussion of the GR evaluation. In particular, we revise the concept of GR navigability, together with a careful discussion of the advantage offered by the new proposed GR-efficiency measure in comparison to the main measures previously adopted in literature. Finally, we clarify and standardize the GR-efficiency terminology in order to simplify and facilitate the discussion in future studies.