Bassett Danielle S, Wymbs Nicholas F, Porter Mason A, Mucha Peter J, Grafton Scott T
Department of Bioengineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA.
Department of Psychology and UCSB Brain Imaging Center, University of California, Santa Barbara, California 93106, USA.
Chaos. 2014 Mar;24(1):013112. doi: 10.1063/1.4858457.
We study the temporal co-variation of network co-evolution via the cross-link structure of networks, for which we take advantage of the formalism of hypergraphs to map cross-link structures back to network nodes. We investigate two sets of temporal network data in detail. In a network of coupled nonlinear oscillators, hyperedges that consist of network edges with temporally co-varying weights uncover the driving co-evolution patterns of edge weight dynamics both within and between oscillator communities. In the human brain, networks that represent temporal changes in brain activity during learning exhibit early co-evolution that then settles down with practice. Subsequent decreases in hyperedge size are consistent with emergence of an autonomous subgraph whose dynamics no longer depends on other parts of the network. Our results on real and synthetic networks give a poignant demonstration of the ability of cross-link structure to uncover unexpected co-evolution attributes in both real and synthetic dynamical systems. This, in turn, illustrates the utility of analyzing cross-links for investigating the structure of temporal networks.
我们通过网络的交叉链接结构来研究网络协同演化的时间共变，为此我们利用超图形式主义将交叉链接结构映射回网络节点。我们详细研究了两组时间网络数据。在一个耦合非线性振荡器网络中，由具有时间共变权重的网络边组成的超边揭示了振荡器群落内部和之间边权重动态的驱动协同演化模式。在人类大脑中，代表学习过程中大脑活动时间变化的网络呈现出早期协同演化，随后随着练习而趋于稳定。超边大小的后续减小与一个自主子图的出现一致，该子图的动态不再依赖于网络的其他部分。我们在真实和合成网络上的结果有力地证明了交叉链接结构在揭示真实和合成动力系统中意外协同演化属性方面的能力。反过来，这也说明了分析交叉链接对于研究时间网络结构的实用性。
