A computational model for signaling pathways in bounded small-world networks corresponding to brain size

A computational model, the bounded composite inverse-d architecture (BCIA), was developed to characterize signaling in small-world networks with large but bounded numbers of nodes, as in human brains. The model is based upon an N-dimensional symmetrical grid with borders, with complete local connections from each node and relatively fewer long-range connections. The length of the signaling pathway generated by a greedy algorithm between two nodes exhibited polylogarithmic behavior when the grid distance between the nodes was less than m, the maximal length of a long-range connection for that network. The simulated length of signaling pathway became linear with internode distance when the grid distance between the two nodes was greater than m. The intensity of long-range connections among nodes was found to be negatively related to the simulated length of signaling pathway. For a constant grid distance between nodes, the average length of a simulated signaling pathway increased with dimension of the BCIA graph. Most strikingly, BCIA simulations of networks with large but bounded numbers (109–1013) of nodes, approximating the number of neurons in the human brain, found that the length of simulated signaling pathway can be substantially shorter than that predicted by the best known asymptotic theoretical bound in small-world networks of infinite size.