  We define a $q$-linear path in a hypergraph $H$ as a sequence
$(e_1,\ldots,e_L)$ of edges of $H$ such that $|e_i \cap e_{i+1}| \in
[\![1,q]\!]$ and $e_i \cap e_j=\varnothing$ if $|i-j|>1$. In this paper, we
study the connected components associated to these paths when $q=k-2$ where $k$
is the rank of $H$. If $k=3$ then $q=1$ which coincides with the well-known
notion of linear path or loose path. We describe the structure of the connected
components, using an algorithmic proof which shows that the connected
components can be computed in polynomial time. We then mention two consequences
of our algorithmic result. The first one is that deciding the winner of the
Maker-Breaker game on a hypergraph of rank 3 can be done in polynomial time.
The second one is that tractable cases for the NP-complete problem of "Paths
Avoiding Forbidden Pairs" in a graph can be deduced from the recognition of a
special type of line graph of a hypergraph.
