图的谱距离
Spectral distances on graphs
摘要：
通过将归一化拉普拉斯算子的谱赋予每个图一个概率测度，并利用概率测度之间的L^p Wasserstein距离，我们定义了所有图的集合上相应的谱距离d_p。这种方法甚至可以扩展到测量无限图之间的距离。本文证明了在伪距离空间中，当图的直径为d_1时，图的直径为1。通过交错不等式进一步研究了d_1在图的大小趋于无穷大时的行为，目的是探索大的真实网络。在模拟中观察到d_1和生物网络的进化距离之间的单调关系。
英文摘要：
By assigning a probability measure via the spectrum of the normalized Laplacian to each graph and using L^p Wasserstein distances between probability measures, we define the corresponding spectral distances d_p on the set of all graphs. This approach can even be extended to measuring the distances between infinite graphs. We prove that the diameter of the set of graphs, as a pseudo-metric space equipped with d_1, is one. We further study the behavior of d_1 when the size of graphs tends to infinity by interlacing inequalities aiming at exploring large real networks. A monotonic relation between d_1 and the evolutionary distance of biological networks is observed in simulations.
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