  We investigated the properties of Boolean networks that follow a given
reliable trajectory in state space. A reliable trajectory is defined as a
sequence of states which is independent of the order in which the nodes are
updated. We explored numerically the topology, the update functions, and the
state space structure of these networks, which we constructed using a minimum
number of links and the simplest update functions. We found that the clustering
coefficient is larger than in random networks, and that the probability
distribution of three-node motifs is similar to that found in gene regulation
networks. Among the update functions, only a subset of all possible functions
occur, and they can be classified according to their probability. More
homogeneous functions occur more often, leading to a dominance of canalyzing
functions. Finally, we studied the entire state space of the networks. We
observed that with increasing systems size, fixed points become more dominant,
moving the networks close to the frozen phase.
