  A pointed graph $(\Gamma,v_0)$ induces a family of transition matrices in
Wildberger's construction of a hermitian hypergroup via a random walk on
$\Gamma$ starting from $v_0$. We will give a necessary condition for producing
a hermitian hypergroup as we assume a weaker condition than the
distance-regularity for $(\Gamma,v_0)$. The condition obtained in this paper
connects the transition matrices and the adjacency matrices associated with
$\Gamma$.
