Spectral Properties Of Networks Research Articles

The impact of pollution transmission networks in a transboundary pollution game

To explore transboundary pollution games with network externalities, this study develops a multi-region differential game which investigates the interaction and co-evolution of multiple pollution stocks across a continuous horizon. Pollution transmission networks are incorporated into the model via an adjacency matrix, detailing transmission paths of pollution across regions. Equilibrium strategies for emissions and investments in pollution control are obtained through a system of coupled differential equations. Our study demonstrates that these equilibrium strategies and the corresponding discounted net welfare of regions depend crucially on the structure of pollution transmission networks. The spectral properties of networks can effectively discern the evolutionary stability of equilibrium strategies. Through a numerical simulation of multiregional pollution dynamics, we also show that regions' motivation for pollution control decreases continuously as their influence in pollution transmission networks (i.e., network influence) increases; Nevertheless, an increase in a region's network influence can significantly reduce local pollution stocks in cycle networks but increase them in tree networks.

Spectrum of Complex Networks

The study of complex networks has been one of the most active fields in science in recent decades. Spectral properties of networks (or graphs that represent them) are of fundamental importance. Researchers have been investigating these properties for many years, and, based on numerical data, have raised a number of questions about the distribution of the eigenvalues and eigenvectors. In this paper, we give the solution to some of these questions. In particular, we determine the limiting distribution of (the bulk of) the spectrum as the size of the network grows to infinity and show that the leading eigenvectors are strongly localized. We focus on the preferential attachment graph, which is the most popular mathematical model for growing complex networks. Our analysis is, on the other hand, general and can be applied to other models

Dependence of Oscillation of Spiking Neural Population on Strength of Inhibitory Feedback

Based on linear-response-like approach and simulations, the relationship between the strength of inhibitory feedback and the oscillation is explored by spectral properties of networks with leaky integrate-and-fire neurons under varying feedback strength. It is found that the network oscillation is enhanced sharply with increasing the feedback strength when the feedback is weak, but is insensitive to the feedback strength when the feedback is not weak. These results suggest that inhibitory feedback plays a limited role in enhancing the network oscillation. A qualitative analysis of the limited role of the inhibitory feedback in enhancing network oscillation is also presented.

Erratum: Spectral properties of networks with community structure [Phys. Rev. E80, 056114 (2009)

Received 25 December 2011DOI:https://doi.org/10.1103/PhysRevE.85.029906©2012 American Physical Society

Spectral properties of networks with community structure

In this paper, we discuss the eigenspectra of networks with community structure. It is shown that in many cases, the spectrum of eigenvalues of the adjacency matrix of a network with community structure gives a clear indication of the number of communities in the network. In particular, for a network with N nodes and N_(c) communities, there will typically be N_(c) eigenvalues that are significantly larger than the magnitudes of all the other (N-N_(c)) eigenvalues. We discuss this property as well as its use and limitations for determining N_(c) .