  We analyze conformational properties of branched polymer structures, formed
on the base of Erd\"os-R\'enyi random graph model. We consider networks with
$N=5$ vertices and variable parameter $c$, that controls graph connectedness.
The universal rotationally invariant size and shape characteristics, such as
averaged asphericity $\langle A_3 \rangle$ and size ratio $g$ of such
structures are obtained both numerically by application of Wei's method and
analytically within the continuous chain model. In particular, our results
quantitatively indicate an increase of asymmetry of polymer network structure
when its connectedness $c$ decreases.
