  $\beta$-skeletons are well-known neighborhood graphs for a set of points. We
extend this notion to sets of line segments in the Euclidean plane and present
algorithms computing such skeletons for the entire range of $\beta$ values. The
main reason of such extension is the possibility to study $\beta$-skeletons for
points moving along given line segments. We show that relations between
$\beta$-skeletons for $\beta > 1$, $1$-skeleton (Gabriel Graph), and the
Delaunay triangulation for sets of points hold also for sets of segments. We
present algorithms for computing circle-based and lune-based $\beta$-skeletons.
We describe an algorithm that for $\beta \geq 1$ computes the $\beta$-skeleton
for a set $S$ of $n$ segments in the Euclidean plane in $O(n^2 \alpha (n) \log
n)$ time in the circle-based case and in $O(n^2 \lambda_4(n))$ in the
lune-based one, where the construction relies on the Delaunay triangulation for
$S$, $\alpha$ is a functional inverse of Ackermann function and $\lambda_4(n)$
denotes the maximum possible length of a $(n,4)$ Davenport-Schinzel sequence.
When $0 < \beta < 1$, the $\beta$-skeleton can be constructed in a $O(n^3
\lambda_4(n))$ time. In the special case of $\beta = 1$, which is a
generalization of Gabriel Graph, the construction can be carried out in a $O(n
\log n)$ time.
