I am reading this article where it explains an ergodic assumption regarding links but I do not quite understand what the autor means.
The “ergodic assumption” of random link switching is of course extremely restrictive, and unlikely to be satisfied by most real systems; thus a snapshot of a temporal information that includes all edges over a fixed time scale can lose a large amount of information: a possible measure of this loss can be found in a comparison of paths in a snapshot and time-respecting paths in the temporal network. In a snapshot, because of the loss of temporal information, we may see paths that are temporally impossible routes of contagion flow, giving us a false idea of the potential infection flow between pairs of nodes. The fraction of snapshot paths that are not time-respecting (and therefore could not transmit infection from the starting to ending nodes) is a rough measure of how important it is to use a temporal network rather than a static snapshot when determining potential infection flow between nodes.
For example, in the cattle trading network in Great Britain, only about half of the paths of two contacts are time-respecting for timeframes over a week, with a substantially smaller fraction being time-respecting for longer paths. The fraction of paths that are temporally possible decreases slightly as longer timeframes are used for the snapshot. When measuring properties of individual nodes, distance in a snapshot therefore may be a poor proxy for disease flow by animal trade between two farms in the Great Britain cattle trading network, and therefore in this case the loss of the temporal information in the static approximation could result in substantially incorrect predictions of disease spread, though it may still give qualitatively useful insight (Kao et al., 2006).
as I understand ergodicity is that an activity is ergodic if the outcome is the same for many people performing it once and one person performing it many times. but I do not quite understand what the author means here