Figure 7

Networks of three nodes. Graphical representation of the thirteen topologically distinct networks of three nodes. Networks are grouped according to their escape times in the limit β → ∞ (see Fig. 8). Node and edge colours are used to highlight the first component of the network (black) as distinct from the rest of the network (grey). For the weakly connected networks (a, b, c), the first component controls the dynamics of the network as a whole. For the strongly connected networks (d, e), the first component is the whole network. (a): Network 1 has one node receiving an input from each of the other nodes. The two black nodes are the first component of the graph but they are themselves disconnected. (b): Networks 2-6 each have a single node in the first component. (c): Networks 7 and 8 each have a strongly connected two-node graph as their first component. (d): Networks 9 and 10 are strongly connected but unbalanced. The number of inputs and outputs are not equal for each individual node. Note that the escape times for these two networks are similar but, unlike those in the other groups, do not converge in the limit β → ∞ (see Figure 8). (e): Networks 11-13 are the strongly connected, balanced networks. For each node, there are as many inputs as outputs.