论文标题
大型有向图的表征和比较通过磁性拉普拉斯的光谱
Characterization and comparison of large directed graphs through the spectra of the magnetic Laplacian
论文作者
论文摘要
在本文中，我们调查了使用磁性laplacian来表征有向图的可能性（又称网络）。获得了许多有趣的结果，包括发现社区结构与一种随机块模型的光谱测量中的旋转对称性有关。由于使用核心多项式方法（kpm），我们在这里显示了磁性拉普拉斯式的墓地特性，我们在这里显示了如何将我们的方法扩展到包含数十万个节点的较大网络。我们还建议将KPM与Wasserstein指标相结合，以测量网络之间的距离，即使这些网络是指向，大且具有不同大小的，这是文献中先前的方法无法解决的硬问题。此外，我们的Python软件包可在\ href {https://github.com/stdogpkg/emate} {github.com/stdogpkg/emate}上公开获得。这些代码可以在CPU和GPU中同时运行，并且即使在具有百万个节点的有向或无向网络中，也可以估计光谱密度和相关的痕量函数，例如熵和埃斯特拉达索引。
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.
