  Random Boolean networks were introduced in 1969 by Kauffman as a model for
gene regulation. By combining analytical arguments and efficient numerical
simulations, we evaluate the properties of relevant components of critical
random Boolean networks independently of update scheme. As known from previous
work, the number of relevant components grows logarithmically with network
size. We find that in most networks all relevant nodes with more than one
relevant input sit in the same component, while all other relevant components
are simple loops. As the proportion of nonfrozen nodes with two relevant inputs
increases, the number of relevant components decreases and the size and
complexity of the largest complex component grows. We evaluate the probability
distribution of different types of complex components in an ensemble of
networks and confirm that it becomes independent of network size in the limit
of large network size. In this limit, we determine analytically the frequencies
of occurence of complex components with different topologies.
