PARALLELISM AND COMPLEXITY OF A SMALL-WORLD NETWORK MODEL

The small-world phenomena exhibits highly localized clustering and short-cut paths between vertices in a graph that reflect observed properties in social networks, epidemiological models and other real-world networks. The small-world models rely on the application of constraint-based randomness or the derivation of constraints on randomness to simulate the desired network complexities and their associated network connection properties. In this paper, rather than exploring the random properties of small-world networks, we employ deterministic strategies in the design of a computationally efficient distributed neuronal-axon network simulator that results in a small world network. These strategies are derived by addressing the parallel complexities of the proposed neuronal-axon network simulator, and also from physical constraints imposed by resource limitations of the distributed simulation architecture. The outcome of this study is the realization of a neuronal-axon network simulator that exhibits small-world characteristics of clustering with a logarithmic degree of separation between nodes without the need for long-range communication edges. The importance of this result is the deterministic application of reasoned optimization rules from which the small-world network emerges.