Fig. 4

Tri-functional networks constructed from the bi-functional networks. a Two extension strategies for constructing tri-functional networks from bi-functional networks. A regulatory node that activates the output node O is adopted as the third input node (e.g., the node M₁); otherwise, a new node R₃ is added to receive the third signal. b The distribution of Q(F₃| F_{1, 2}) for all tri-functional networks obtained, with 141 tri-functional networks with Q(F₃| F_{1, 2})> 500 (marked by dashed red box. c Structure diagram of all tri-functional networks for illustrating their structure relationships. The blue, green, and red colors represent six-, five- and four-node networks, respectively. Small and large dots represent tri-functional networks with Q(F₃| F_{1, 2})> 100, and Q(F₃| F_{1, 2})> 500, respectively. They are organized along the vertical axis with respect to the number of links in the network. Several network topologies with the least number of links are highlighted at the bottom