论文标题
特征向量在超图中的定位：配对与高阶链接
Eigenvector localization in hypergraphs: pair-wise vs higher-order links
论文作者
论文摘要
复杂网络的拉普拉斯特征向量的定位行为为相应的复杂系统上的各种动态现象提供了理解。我们在数值上研究了Hyperedges在驱动超图形laplacians的特征向量定位中的作用。通过定义单个参数γ，该参数γ，该参数可以测量成对和高阶相互作用的相对强度，我们分析了相互作用对定位特性的影响。对于，γ<1，成对链接对特征向量定位的影响没有影响，而高阶相互作用则刺激了较大的特征值中的定位。对于γ> 1，成对的相互作用会导致对应于小特征值的特征向量的定位，尽管较高级别的相互作用虽然比配对链接要小得多，但仍在继续推动与较大特征值相对应的特征向量的定位。结果对于理解动态现象（例如扩散）以及在具有高阶相互作用的一系列现实世界复合系统上随机步行将很有用。
Localization behaviours of Laplacian eigenvectors of complex networks provide understanding to various dynamical phenomena on the corresponding complex systems. We numerically investigate role of hyperedges in driving eigenvector localization of hypergraphs Laplacians. By defining a single parameter γwhich measures the relative strengths of pair-wise and higher-order interactions, we analyze the impact of interactions on localization properties. For, γ< 1 there exists no impact of pairwise links on eigenvector localization while the higher-order interactions instigate localization in the larger eigenvalues. For γ> 1, pair-wise interactions cause localization of eigenvector corresponding to small eigenvalues, where as higherorder interactions, despite being much lesser than the pair-wise links, keep driving localization of the eigenvectors corresponding to larger eigenvalues. The results will be useful to understand dynamical phenomena such as diffusion, and random walks on a range of real-world complex systems having higher-order interactions.
