SIAM Journal on Applied Dynamical Systems, Volume 19, Issue 2, Page 1057-1079, January 2020.
In this work, we introduce a new Laplacian matrix, referred to as the hubs-attracting Laplacian, accounting for diffusion processes on networks where the hopping of a particle occurs with higher probability from low to high degree nodes. This notion complements the one of the hubs-repelling Laplacian discussed in [E. Estrada, Linear Algebra Appl., 596 (2020), pp. 256--280], that considers the opposite scenario, with higher hopping probabilities from high to low degree nodes. We formulate a model of oscillators coupled through the new Laplacian and study the synchronizability of the network through the analysis of the spectrum of the Laplacian. We discuss analytical results providing bounds for the quantities of interest for synchronization and computational results showing that the hubs-attracting Laplacian generally has better synchronizability properties when compared to the classical one, with a low occurrence rate for the graphs where this is not true. Finally, two illustrative case studies of synchronization through the hubs-attracting Laplacian are considered.

中文翻译：

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网络上吸引集线器的拉普拉斯算子和相关同步

SIAM应用动力系统杂志，第19卷，第2期，第1057-1079页，2020年1月。
在这项工作中，我们引入了一个新的拉普拉斯矩阵，称为吸引集线器的拉普拉斯矩阵，该矩阵说明了网络中的扩散过程，其中从低到高节点发生粒子跳跃的可能性更高。这个概念补充了[E. Estrada，Linear Algebra Appl。，596（2020），pp.256--280]，它考虑了相反的情况，即从高阶节点到低阶节点的跳变概率更高。我们建立了一个通过新的拉普拉斯算子耦合的振荡器模型，并通过分析拉普拉斯算子的频谱研究了网络的同步性。我们讨论的分析结果为同步的关注量提供了界线，并且计算结果表明，与经典轮毂相比，吸引轮毂的拉普拉斯算子通常具有更好的同步性，而图的出现率很低，这是不正确的。最后，考虑了通过吸引集线器的拉普拉斯算子进行同步的两个说明性案例研究。