  The notion of $f$-ideal is recent and has so far been studied in several
papers. In \cite{qfi}, the idea of $f$-ideal is generalized to quasi
$f$-ideals, which is much larger class than the class of $f$-ideals. In this
paper, we introduce the concept of quasi $f$-simplicial complex and quasi
$f$-graph. We give a characterization of quasi $f$-graphs on $n$ vertices. A
complete solution of connectedness of quasi $f$-simplicial complexes is
described. We have also shown a method of constructing Cohen-Macaulay quasi
$f$-graphs.
