Introduction

Computer simulation of the activity of complex neural networks representing substantial portions of the brain is limited by a number of practical considerations, notably the capacity of existing computers and the finite human resources available for analysis of a proliferating output. Whatever the specific model chosen, whether operating in discrete or continuous time, and whether involving the firing states or the firing rates of neurons as the basic dynamical variables, there will arise the possibility that ‘edge effects’ seriously diminish the relevance of the simulation to the behavior of the actual biological system. Such effects may arise, principally, from the fact that the number of neuronal elements in the simulation is too small, or, secondarily, from the fact that the numbers of synaptic inputs to given elements are inappropriate.

In this contribution we shall make an attempt to quantify edge effects in terms of a simple conception of interneuronal distance, reasoning that the asymptotic autonomous behavior of neural models will hinge critically on the topological properties of the net. This will be especially true of the repertoire of cyclic modes (Clark, Rafelski & Winston, 1985) of an assembly of N binary threshold elements operating syncronously in discrete time. As a first approximation to a meaningful definition of the distance dki from neuron i to neuron k in such models, one may use simply the minimum number of synaptic junctions which information must traverse in going from i to k.