Fig. 4

Examples of graph products: \(K_{4}\,\square \, C_{8}\) (top-left panel), \(K_{4}\otimes C_{8}\) (top-right), \(K_{4}\boxtimes C_{8}\) (bottom-left), \(K_{4}\bullet C_{8}\) (bottom-right). The figure shows the differences between the different products, in particular the number of connections per neuron, which is, respectively, \(M_{K_{4}}+M_{C_{8}}=5\), \(M_{K_{4}}M_{C_{8}}=6\), \((M_{K_{4}}+1 ) (M_{C_{8}}+1 )-1=11\), \(M_{K_{4}}N_{C_{8}}+M_{C_{8}}=26\) (some connections may be overlapping). In general, a product between two graphs \(\mathcal{G}\), \(\mathcal{H}\) can be interpreted as a system of \(N_{\mathcal{G}}\) neural populations with \(N_{\mathcal{H}}\) neurons each, interconnected in different ways according to the graph product that has been chosen