title: Sample-to-sample fluctuations in real-network ensembles.
abstract: 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.
authors: Department of Physics and Redwood Center for Theoretical Neuroscience, University of California, Berkeley, California 94720, USA.
authors: Nicole
authors: N
authors: Carlson
authors: Dong-Hee
authors: DH
authors: Kim
authors: Adilson E
authors: AE
authors: Motter