  Using Penrose binor calculus for $SU(2)$ ($SL(2,C)$) tensor expressions, a
graphical method for the connection representation of Euclidean Quantum Gravity
(real connection) is constructed. It is explicitly shown that: {\it (i)} the
recently proposed scalar product in the loop-representation coincide with the
Ashtekar-Lewandoski cylindrical measure in the space of connections; {\it (ii)}
it is possible to establish a correspondence between the operators in the
connection representation and those in the loop representation. The
construction is based on embedded spin network, the Penrose graphical method of
$SU(2)$ calculus, and the existence of a generalized measure on the space of
connections modulo gauge transformations.
