基于磁拉普拉斯算子谱的大型有向图的刻画与比较
Characterization and comparison of large directed graphs through the spectra of the magnetic Laplacian
摘要：
在本文中，我们研究了使用磁拉普拉斯算子来表征有向图（a.k.a.）的可能性。网络）。得到了许多有趣的结果，包括发现了一类随机块体模型的谱测量中，群落结构与旋转对称性有关。由于磁拉普拉斯算子的厄米性，我们在这里展示了如何使用核多项式方法（KPM）将我们的方法扩展到包含数十万节点的大型网络。我们还建议将KPM与Wasserstein度量相结合，以测量网络之间的距离，即使这些网络是有向的，大的，有不同的大小，一个很难的问题，不能解决以前的方法在文献中提出的。此外，我们的python包在\href{https://github.com/stdogpkg/emate}{github.com/stdogpkg/emate}上公开提供。这些代码可以在CPU和GPU上运行，并且可以估计谱密度和相关的迹函数，例如熵和Estrada指数，即使在具有数百万节点的有向或无向网络中。
英文摘要：
In this paper we investigated the possibility to use the magnetic Laplacian to characterize directed graphs (a.k.a. networks). Many interesting results are obtained, including the finding that community structure is related to rotational symmetry in the spectral measurements for a type of stochastic block model. Due the hermiticity property of the magnetic Laplacian we show here how to scale our approach to larger networks containing hundreds of thousands of nodes using the Kernel Polynomial Method (KPM). We also propose to combine the KPM with the Wasserstein metric in order to measure distances between networks even when these networks are directed, large and have different sizes, a hard problem which cannot be tackled by previous methods presented in the literature. In addition, our python package is publicly available at \href{https://github.com/stdogpkg/emate}{github.com/stdogpkg/emate}. The codes can run in both CPU and GPU and can estimate the spectral density and related trace functions, such as entropy and Estrada index, even in directed or undirected networks with million of nodes.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
