In biometrics research, the periocular region has been regarded as an interesting trade-off between the face and the iris, particularly in unconstrained data acquisition setups. As in other biometric traits, the current challenge is the development of more robust recognition algorithms. Having investigated the suitability of the 'elastic graph matching' (EGM) algorithm to handle nonlinear distortions in the periocular region because of facial expressions, the authors observed that vertices locations often not correspond to displacements in the biological tissue. Hence, they propose a 'globally coherent' variant of EGM (GC-EGM) that avoids sudden local angular movements of vertices while maintains the ability to faithfully model non-linear distortions. Two main adaptations were carried out: (i) a new term for measuring vertices similarity and (ii) a new term in the edges-cost function penalises changes in orientation between the model and test graphs. Experiments were carried out both in synthetic and real data and point for the advantages of the proposed algorithm. Also, the recognition performance when using the EGM and GC-EGM was compared, and statistically significant improvements in the error rates were observed when using the GC-EGM variant..