Boolean network topologies and the determinative power of nodes

Boolean networks have been used extensively for modelling networks whose node activity could be simplified to a binary outcome, such as on–off. Each node is influenced by the states of the other nodes via a logical Boolean function. The network is described by its topological properties which refer to the links between nodes, and its dynamical properties which refer to the way each node uses the information obtained from other nodes to update its state. This work explores the correlation between the information stored in the Boolean functions for each node in a property known as the determinative power (DP) and some topological properties of each node, in particular the clustering coefficient and the betweenness centrality. The DP of nodes is defined using concepts from information theory, in particular the mutual information. The primary motivation is to construct models of real-world networks to examine if the DP is sensitive to any of the considered topological properties. The findings indicate that, for a homogeneous network in which all nodes obey the same threshold function under three different topologies, the DP can have a negative correlation with the clustering coefficient and a positive correlation with the betweenness centrality, depending on the topological properties of the network. A statistical analysis on a collection of 36 Boolean models of signal transduction networks reveals that the correlations observed in the theoretical cases are suppressed in the biological networks, thus supporting previous research results.