Temporal lobe epilepsy is a brain network disorder characterized by alterations at both the structural and the functional levels. It remains unclear how structure and function are related and whether this has any clinical relevance. In the present work, we adopted a novel methodological approach investigating how network structural features influence the large-scale dynamics. The functional network was defined by the spatio-temporal spreading of aperiodic bursts of activations (neuronal avalanches), as observed utilizing high-density electroencephalography in patients with temporal lobe epilepsy. The structural network was modelled as the region-based thickness covariance. Loosely speaking, we quantified the similarity of the cortical thickness of any two brain regions, both across groups and at the individual level, the latter utilizing a novel approach to define the subject-wise structural covariance network. In order to compare the structural and functional networks (at the nodal level), we studied the correlation between the probability that a wave of activity would propagate from a source to a target region and the similarity of the source region thickness as compared with other target brain regions. Building on the recent evidence that large-waves of activities pathologically spread through the epileptogenic network in temporal lobe epilepsy, also during resting state, we hypothesize that the structural cortical organization might influence such altered spatio-temporal dynamics. We observed a stable cluster of structure-function correlation in the bilateral limbic areas across subjects, highlighting group-specific features for left, right and bilateral temporal epilepsy. The involvement of contralateral areas was observed in unilateral temporal lobe epilepsy. We showed that in temporal lobe epilepsy, alterations of structural and functional networks pair in the regions where seizures propagate and are linked to disease severity. In this study, we leveraged on a well-defined model of neurological disease and pushed forward personalization approaches potentially useful in clinical practice. Finally, the methods developed here could be exploited to investigate the relationship between structure-function networks at subject level in other neurological conditions.