在共享给定度分布和全局聚类的网络中映射结构多样性：基于Diophantine方程突变的自适应分辨率网格搜索进化
Mapping structural diversity in networks sharing a given degree distribution and global clustering: Adaptive resolution grid search evolution with Diophantine equation-based mutations
摘要：
生成共享给定度分布和全局聚类的网络的方法可以引起结构属性的变化，而不是控制。结构特性的多样性反过来又会影响在这些网络上运行的动态过程的结果。由于详尽的采样是不可能的，我们提出了一个新的进化框架映射这种结构的多样性。该框架的三个主要特征是：（a）基于子图的网络编码，（b）基于求解丢番图方程系统的精确突变，以及（c）启发式多样性驱动机制，以驱动MapElite算法中的分辨率变化。我们表明，我们的框架可以引发网络的多样性，在其高阶结构，这种多样性影响的行为的复杂传染模型。通过与最先进的集群网络生成方法的比较，我们证明了我们的方法可以发现一个不同的网络，而不需要计算上不可行的混合时间。此外，我们认为，基于子图的编码提供了更大的信心，高阶网络结构的多样性为低数量的样本，是解释我们的结果与复杂的传染模型的基础。我们相信，这个框架可以适用于其他复杂的景观，实际上不能通过详尽的采样映射。
英文摘要：
Methods that generate networks sharing a given degree distribution and global clustering can induce changes in structural properties other than that controlled for. Diversity in structural properties, in turn, can affect the outcomes of dynamical processes operating on those networks. Since exhaustive sampling is not possible, we propose a novel evolutionary framework for mapping this structural diversity. The three main features of this framework are: (a) subgraph-based encoding of networks, (b) exact mutations based on solving systems of Diophantine equations, and (c) heuristic diversity-driven mechanism to drive resolution changes in the MapElite algorithm. We show that our framework can elicit networks with diversity in their higher-order structure and that this diversity affects the behaviour of the complex contagion model. Through a comparison with state of the art clustered network generation methods, we demonstrate that our approach can uncover a comparably diverse range of networks without needing computationally unfeasible mixing times. Further, we suggest that the subgraph-based encoding provides greater confidence in the diversity of higher-order network structure for low numbers of samples and is the basis for explaining our results with complex contagion model. We believe that this framework could be applied to other complex landscapes that cannot be practically mapped via exhaustive sampling.
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