  Using the bond fluctuation model we study polymer networks obtained by
endlinking of symmetric 4-arm star polymers. We consider two types of systems.
Solutions of one type (A) of star polymers and solution of two types (A,B) of
star polymer where A-type polymers can only crosslink with B-type polymers. We
find that network defects in $A$ networks are dominated by short dangling loops
close to overlap concentration $c^{*}$. $AB$ networks develop a more perfect
network structure, since loop sizes involving an odd number of stars are
impossible, and thus, the most frequent dangling loop with largest impact on
the phantom modulus is absent. The analysis of the pair-correlation and
scattering function reveals that there is an amorphous packing of $A$ and $B$
type stars with a homogenization of $A$ and $B$ concentrations upon
cross-linking at intermediate length scales in contrast to the previously
suggested crystalline like order of $A$ and $B$ components at $c^{*}$. This
result is corroborated by the coincidence of the probabilities of the shortest
loop structures (which is impossible upon the previously suggested packing of
stars) in both types of networks.
  Furthermore, we derive the vector order parameters associated with the most
frequent network structures based on the phantom model. In particular, for $AB$
networks we can show that there is a dominating cyclic defect with a clearly
separated order parameter that could be used to analyze cyclic network defects.
