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Let 
$R$ be a commutative ring. The regular digraph of ideals of 
$R$, denoted by 
$\Gamma (R)$, is a digraph whose vertex set is the set of all nontrivial ideals of 
$R$ and, for every two distinct vertices 
$I$ and 
$J$, there is an arc from 
$I$ to 
$J$ whenever 
$I$ contains a nonzero divisor on 
$J$. In this paper, we study the connectedness of 
$\Gamma (R)$. We also completely characterise the diameter of this graph and determine the number of edges in 
$\Gamma (R)$, whenever 
$R$ is a finite direct product of fields. Among other things, we prove that 
$R$ has a finite number of ideals if and only if 
$\mathrm {N}_{\Gamma (R)}(I)$ is finite, for all vertices 
$I$ in 
$\Gamma (R)$, where 
$\mathrm {N}_{\Gamma (R)}(I)$ is the set of all adjacent vertices to 
$I$ in 
$\Gamma (R)$.
