Interactive programming environments are powerful tools for promoting innovative network thinking, teaching science of complexity, and exploring emergent phenomena. This paper reports on our recent development of the deterministic random walk model in NetLogo, a leading platform for computational thinking, eco-system thinking, and multi-agent cross-platform programming environment. The deterministic random walk is foundational to modeling dynamical processes on complex networks. Inspired by the temporal visualizations offered in NetLogo, we investigated the relationship between network topology and diffusion saturation time for the deterministic random walk model. Our analysis uncovers that in Erd\H{o}s-R\'{e}nyi graphs, the saturation time exhibits an asymmetric pattern with a considerable probability of occurrence. This behavior occurs when the hubs, defined as nodes with relatively higher number of connections, emerge in Erd\H{o}s-R\'{e}nyi graphs. Yet, our analysis yields that the hubs in Barab\'{a}si-Albert model stabilize the the convergence time of the deterministic random walk model. These findings strongly suggest that depending on the dynamical process running on complex networks, complementing characteristics other than the degree need to be taken into account for considering a node as a hub. We have made our development open-source, available to the public at no cost at https://github.com/bravandi/NetLogo-Dynamical-Processes.

翻译：交互式编程环境是促进创新网络思维、教授复杂性科学以及探索涌现现象的强大工具。本文报告了我们近期在NetLogo（一个领先的计算思维、生态系统思维及多智能体跨平台编程环境）中开发的确定性随机游走模型。确定性随机游走是复杂网络上动态过程建模的基础。受NetLogo提供的时序可视化启发，我们研究了确定性随机游走模型中网络拓扑与扩散饱和时间之间的关系。我们的分析揭示，在Erdős–Rényi图中，饱和时间表现出一种非对称模式，且具有相当高的出现概率。当Erdős–Rényi图中出现枢纽节点（即连接数相对较高的节点）时，这种行为便会发生。然而，我们的分析还发现，Barabási–Albert模型中的枢纽节点反而稳定了确定性随机游走模型的收敛时间。这些发现强烈表明，根据复杂网络上运行的动态过程，在将节点视为枢纽时，除了节点度之外，还需要考虑其他互补特性。我们已将开发成果开源，并在https://github.com/bravandi/NetLogo-Dynamical-Processes上免费向公众提供。