  In a temporal network causal paths are characterized by the fact that links
from a source to a target must respect the chronological order. In this article
we study the causal paths structure in temporal networks of human face to face
interactions in different social contexts. In a static network paths are
transitive i.e. the existence of a link from $a$ to $b$ and from $b$ to $c$
implies the existence of a path from $a$ to $c$ via $b$. In a temporal network
the chronological constraint introduces time correlations that affects
transitivity. A probabilistic model based on higher order Markov chains shows
that correlations that can invalidate transitivity are present only when the
time gap between consecutive events is larger than the average value and are
negligible below such a value. The comparison between the densities of the
temporal and static accessibility matrices shows that the static representation
can be used with good approximation. Moreover, we quantify the extent of the
causally connected region of the networks over time.
