论文标题
高阶相互作用形状的集体动力学在超图和简单复合物中不同
Higher-order interactions shape collective dynamics differently in hypergraphs and simplicial complexes
论文作者
论文摘要
高阶网络已成为建模复杂系统及其集体行为的强大框架。除了成对的相互作用之外，它们还通过诸如简单复合物和超图像等表示的任意数量单位之间编码结构化关系。到目前为止，简单络合物和超图之间的选择通常是由技术便利的动机。在这里，以同步为例，我们证明了高阶相互作用的效果高度代表性依赖性。特别是，高阶相互作用通常会增强超图中的同步，但在简单络合物中具有相反的效果。我们通过将不同的超图结构的同步性与（广义）程度异质性和跨阶度相关性联系起来，从而提供理论见解，这反过来又影响了从传播到扩散的广泛动力学过程。我们的发现揭示了高阶表示对集体动力学的隐藏影响，突出了在研究与非局部相互作用的系统时选择适当表示的重要性。
Higher-order networks have emerged as a powerful framework to model complex systems and their collective behavior. Going beyond pairwise interactions, they encode structured relations among arbitrary numbers of units through representations such as simplicial complexes and hypergraphs. So far, the choice between simplicial complexes and hypergraphs has often been motivated by technical convenience. Here, using synchronization as an example, we demonstrate that the effects of higher-order interactions are highly representation-dependent. In particular, higher-order interactions typically enhance synchronization in hypergraphs but have the opposite effect in simplicial complexes. We provide theoretical insight by linking the synchronizability of different hypergraph structures to (generalized) degree heterogeneity and cross-order degree correlation, which in turn influence a wide range of dynamical processes from contagion to diffusion. Our findings reveal the hidden impact of higher-order representations on collective dynamics, highlighting the importance of choosing appropriate representations when studying systems with nonpairwise interactions.
