Adaptive networks model social, physical, technical, or biological systems as attributed graphs evolving at the level of both their topology and data. They are naturally described by graph transformation, but the majority of authors take an approach inspired by the physical sciences, combining an informal description of the operations with programmed simulations, and systems of ODEs as the only abstract mathematical description. We show that we can capture a range of social network models, the so-called voter models, as stochastic attributed graph transformation systems, demonstrate the benefits of this representation and establish its relation to the non-standard probabilistic view adopted in the literature. We use the theory and tools of graph transformation to analyze and simulate the models and propose a new variant of a standard stochastic simulation algorithm to recreate the results observed.
翻译:适应性网络模式社会、物理、技术或生物系统模式,作为在地形和数据水平上演进的推算图,自然地通过图解转换加以描述,但大多数作者采取由物理科学启发的方法,将操作的非正式描述与编程模拟相结合,将脱氧核糖核糖核酸系统作为唯一的抽象数学描述。我们显示,我们可以捕捉一系列社会网络模型,即所谓的选民模型,作为随机推算图转换系统,展示这种表达的效益,并确立其与文献中采用的非标准概率性观点的关系。我们利用图解转换理论和工具分析和模拟模型,并提出新的标准蒸汽模拟算法变方,以重建观察到的结果。