| Summary: | To model agent relationships in agent-based models, it is often necessary to incorporate a social network whose topology is commonly assumed to be "small-world." This is potentially problematic, as the classification is broad and covers a wide-range of network statistics. Furthermore, real networks are often dynamic, in that edges and nodes can appear or disappear, and spatial, in that connections are influenced by an agent's position within a particular social space. These properties are difficult to achieve in current network formation tools. We have, therefore, developed a novel social network formation model, that creates and dynamically adjusts small-world networks using local spatial interactions, while maintaining tunable global network statistics from across the broad space of possible small-world networks. It is, therefore, a useful tool for multiagent simulations and diffusion processes, particularly those in which agents and edges die or are constrained in their movement within some social space. We also show, using a simple epidemiological diffusion model, that a range of networks can all satisfy the small-world criterion, but behave quite differently. This demonstrates that it is problematic to generalize results across the whole space of small-world networks
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