Abstract
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.
Highlights
A small-world network is the notion that a short chain of intermediate acquaintances, which is characterized by a separation length of about six steps, can connect almost any pair of people in the world to one another
Small-world models for social networks display a large clustering coefficient; a high local clustering with disjoint regions that on average are connected to any node by only a few steps
This paper presents a different perspective in the understanding of small-world models by examining the design of a neuronal network simulator that is found to exhibits small-world features
Summary
A small-world network is the notion that a short chain of intermediate acquaintances, which is characterized by a separation length of about six steps, can connect almost any pair of people in the world to one another. This paper presents an overview of small-world models, based on rules applied with small random probabilities. This approach makes sense if Nature is truly a stochastic process [7]. This paper presents a different perspective in the understanding of small-world models by examining the design of a neuronal network simulator that is found to exhibits small-world features. In the remainder of this paper, we present the notion of six degrees of separation, current small-world models, and in particular the design of a neuronal-axon network simulator, its small-world organization, and the emergence of the small world from the application of optimization considerations
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