  We present new quantum algorithms for Triangle Finding improving its best
previously known quantum query complexities for both dense and spare
instances.For dense graphs on $n$ vertices, we get a query complexity of
$O(n^{5/4})$ without any of the extra logarithmic factors present in the
previous algorithm of Le Gall [FOCS'14]. For sparse graphs with $m\geq n^{5/4}$
edges, we get a query complexity of $O(n^{11/12}m^{1/6}\sqrt{\log n})$, which
is better than the one obtained by Le Gall and Nakajima [ISAAC'15] when $m \geq
n^{3/2}$. We also obtain an algorithm with query complexity ${O}(n^{5/6}(m\log
n)^{1/6}+d_2\sqrt{n})$ where $d_2$ is the variance of the degree distribution.
Our algorithms are designed and analyzed in a new model of learning graphs that
we call extended learning graphs. In addition, we present a framework in order
to easily combine and analyze them. As a consequence we get much simpler
algorithms and analyses than previous algorithms of Le Gall {\it et al} based
on the MNRS quantum walk framework [SICOMP'11].
