Graphs with diverse structural characteristics play a central role in modelling and optimization tasks. The ability to generate different types of graphs that exhibit shared properties is likewise essential for algorithm selection and configuration. However, constructing graphs that preserve high-level properties across a broad range of graph classes remains a challenging problem. We present a novel evolutionary approach to evolve graphs based on the Laplacian graph spectra descriptor. This descriptor can be used as part of a fitness function to evaluate graphs according to their desired high-level properties. Our evolutionary algorithm evolves graphs towards this descriptor in order to obtain graphs having properties that are consistent with it but are different from each other in terms of non-spectral graph metrics, such as path length, clustering coefficient and betweenness centrality. Our experimental results show that our approach is successful for different classes of graphs and a wide range of Laplacian graph spectra.

翻译：具有多样化结构特征的图在建模和优化任务中扮演着核心角色。生成具有共享属性的不同类型图的能力同样对算法选择与配置至关重要。然而，构建能够保留跨广泛图类高层次属性的图仍是一个具有挑战性的问题。我们提出了一种新颖的进化方法，基于拉普拉斯图谱描述符来进化图。该描述符可作为适应度函数的一部分，根据期望的高层次属性评估图。我们的进化算法使图向此描述符进化，以获取具有与其一致属性但图度量指标（如路径长度、聚类系数和介数中心性）互异的图。实验结果表明，该方法适用于不同图类及广泛的拉普拉斯图谱。