  We apply complex network analysis to the state spaces of random Boolean
networks (RBNs). An RBN contains $N$ Boolean elements each with $K$ inputs. A
directed state space network (SSN) is constructed by linking each dynamical
state, represented as a node, to its temporal successor. We study the
heterogeneity of an SSN at both local and global scales, as well as
sample-to-sample fluctuations within an ensemble of SSNs. We use in-degrees of
nodes as a local topological measure, and the path diversity [Phys. Rev. Lett.
98, 198701 (2007)] of an SSN as a global topological measure. RBNs with $2 \leq
K \leq 5$ exhibit non-trivial fluctuations at both local and global scales,
while K=2 exhibits the largest sample-to-sample, possibly non-self-averaging,
fluctuations. We interpret the observed ``multi scale'' fluctuations in the
SSNs as indicative of the criticality and complexity of K=2 RBNs. ``Garden of
Eden'' (GoE) states are nodes on an SSN that have in-degree zero. While
in-degrees of non-GoE nodes for $K>1$ SSNs can assume any integer value between
0 and $2^N$, for K=1 all the non-GoE nodes in an SSN have the same in-degree
which is always a power of two.
