  The `spider theorem' for a general Frobenius algebra $A$, classifies all maps
$A^{\otimes m}\to A^{\otimes n}$ that are built from the operations and, in a
graphical representation, represented by a {\it connected} diagram. Here the
algebra can be noncommutative and the Frobenius form can be asymmetric. We view
this theorem as reducing any connected diagram to a standard form with $j$
beads $B$, where $j$ is the number of bounded connected components of the
original diagram. We study the associated F-dimension Hilbert series
$\dim_x=\sum_{j=0}^\infty x^j\dim_j$, where $\dim_j=\epsilon\circ B^j\circ 1$
are invariants of the Frobenius structure. We also study moduli of asymmetric
quasispecial and `weakly symmetric' Frobenius structures and their
F-dimensions. Examples include general Frobenius structures on matrix algebras
$A=M_d(k)$ and on group algebras $k G$ as well as on $u_q(sl_2)$ at low roots
of unity.
