Department of Physics and Redwood Center for Theoretical Neuroscience, University of California, Berkeley, California 94720, USA.
Chaos. 2011 Jun;21(2):025105. doi: 10.1063/1.3602223.
Network modeling based on ensemble averages tacitly assumes that the networks meant to be modeled are typical in the ensemble. Previous research on network eigenvalues, which govern a range of dynamical phenomena, has shown that this is indeed the case for uncorrelated networks with minimum degree ≥ 3. Here, we focus on real networks, which generally have both structural correlations and low-degree nodes. We show that: (i) the ensemble distribution of the dynamically most important eigenvalues can be not only broad and far apart from the real eigenvalue but also highly structured, often with a multimodal rather than a bell-shaped form; (ii) these interesting properties are found to be due to low-degree nodes, mainly those with degree ≤ 3, and network communities, which is a common form of structural correlation found in real networks. In addition to having implications for ensemble-based approaches, this shows that low-degree nodes may have a stronger influence on collective dynamics than previously anticipated from the study of computer-generated networks.
基于集合平均的网络建模隐含地假设，所建模的网络在集合中是典型的。以前关于网络特征值的研究，这些特征值控制着一系列动态现象，已经表明对于具有最小度≥3 的无关联网络，情况确实如此。在这里，我们专注于具有结构相关性和低度数节点的真实网络。我们表明：(i)动态最重要特征值的集合分布不仅可能很宽，与实际特征值相差甚远，而且还具有高度的结构性，通常呈多峰而不是钟形；(ii)这些有趣的性质归因于低度数节点，主要是那些度数≤3 的节点，以及网络社区，这是真实网络中常见的结构相关性形式。除了对基于集合的方法有影响外，这表明低度数节点对集体动力学的影响可能比以前从计算机生成网络的研究中预期的要大。
