  In this paper, we study the restrictions of both the harmonic functions and
the eigenfunctions of the symmetric Laplacian to edges of pre-gaskets contained
in the Sierpinski gasket. For a harmonic function, its restriction to any edge
is either monotone or having a single extremum. For an eigenfunction, it may
have several local extrema along edges. We prove general criteria, involving
the values of any given function at the endpoints and midpoint of any edge, to
determine which case it should be, as well as the asymptotic behavior of the
restriction near the endpoints. Moreover, for eigenfunctions, we use spectral
decimation to calculate the exact number of the local extrema along any edge.
This confirm, in a more general situation, a conjecture of K. Dalrymple, R.S.
Strichartz and J.P. Vinson \cite{DSV} on the behavior of the restrictions to
edges of the basis Dirichlet eigenfunctions, suggested by the numerical data.
