  The first known families of cages arised from the incidence graphs of
generalized polygons of order $q$, $q$ a prime power. In particular,
$(q+1,6)$--cages have been obtained from the projective planes of order $q$.
Morever, infinite families of small regular graphs of girth 5 have been
constructed performing algebraic operations on $\mathbb{F}_q$.
  In this paper, we introduce some combinatorial operations to construct new
infinite families of small regular graphs of girth 7 from the $(q+1,8)$--cages
arising from the generalized quadrangles of order $q$, $q$ a prime power.
