  In this paper, we introduce the notion of two-way $(t,\lambda)$-liking
digraphs as a way to extend the results for generalized friendship graphs.
  A two-way $(t,\lambda)$-liking digraph is a digraph in which every $t$
vertices have exactly $\lambda$ common out-neighbors and $\lambda$ common
in-neighbors.
  We first show that if $\lambda \ge 2$, then a two-way $(2,\lambda)$-liking
digraph of order $n$ is $k$-diregular for a positive integer $k$ satisfying the
equation $(n-1)\lambda=k(k-1)$.
  This result is comparable to the result by Bose and Shrikhande in 1969 and
actually extends it.
  Another main result is that if $t \ge 3$, then the complete digraph on
$t+\lambda$ vertices is the only two-way $(t,\lambda)$-liking digraph.
  This result can stand up to the result by Carstens and Kruse in 1977 and
essentially extends it.
  In addition, we find that two-way $(t, \lambda)$-liking digraphs are closely
linked to symmetric block designs and extend some existing results of $(t,
\lambda)$-liking digraphs.
