Spectral density of complex networks with two species of nodes

@article{Nagao2013SpectralDO,
  title={Spectral density of complex networks with two species of nodes},
  author={Taro Nagao},
  journal={Journal of Physics A: Mathematical and Theoretical},
  year={2013},
  volume={46}
}
  • T. Nagao
  • Published 25 August 2012
  • Computer Science, Physics
  • Journal of Physics A: Mathematical and Theoretical
The adjacency and Laplacian matrices of complex networks with two species of nodes are studied and the spectral density is evaluated by using the replica method in statistical physics. The network nodes are classified into two species (A and B) and connections are made only between the nodes of different species. A static model of such bipartite networks with power law degree distributions is introduced by applying Goh, Kahng and Kim’s method to construct scale-free networks. As a result, the… 
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2 Citations

Finite-size corrections to the spectrum of regular random graphs: An analytical solution.

TLDR
A thorough analytical study of the O(1/N) correction to the spectrum of regular random graphs with N→∞ nodes with isolated eigenvalue is developed, which exhibits an excellent agreement between this analytical formula and direct diagonalization results.

Extreme eigenvalues of sparse, heavy tailed random matrices

References

SHOWING 1-10 OF 32 REFERENCES

Spectral density of complex networks with a finite mean degree

In order to clarify the statistical features of complex networks, the spectral density of adjacency matrices has often been investigated. Adopting a static model introduced by Goh, Kahng and Kim, we…

Spectral densities of scale-free networks.

The spectral densities of the weighted Laplacian, random walk, and weighted adjacency matrices associated with a random complex network are studied using the replica method. The link weights are…

Eigenvalue spectra of complex networks

We examine the eigenvalue spectrum, ρ(μ), of the adjacency matrix of a random scale-free network with an average of p edges per vertex using the replica method. We show how in the dense limit, when p…

Spectra of complex networks.

TLDR
It is shown that spectra of locally treelike random graphs may serve as a starting point in the analysis of spectral properties of real-world networks, e.g., of the Internet.

Emergence of scaling in random networks

TLDR
A model based on these two ingredients reproduces the observed stationary scale-free distributions, which indicates that the development of large networks is governed by robust self-organizing phenomena that go beyond the particulars of the individual systems.

Statistical mechanics of complex networks

TLDR
A simple model based on these two principles was able to reproduce the power-law degree distribution of real networks, indicating a heterogeneous topology in which the majority of the nodes have a small degree, but there is a significant fraction of highly connected nodes that play an important role in the connectivity of the network.

Random networks: eigenvalue spectra

Self-organization of collaboration networks.

TLDR
A model of a growing network, which combines preferential edge attachment with the bipartite structure, generic for collaboration networks is proposed, which depends exclusively on basic properties of the network, such as the total number of collaborators and acts of collaboration, the mean size of collaborations, etc.

Spectra of modular random graphs

We compute spectra of symmetric random matrices defined on graphs exhibiting a modular structure. Modules are initially introduced as fully connected sub-units of a graph. By contrast, inter-module…

Spectra of modular and small-world matrices

TLDR
For small-world networks, it is found that the introduction of short cuts can lead to the creation of satellite bands outside the central band of extended states, exhibiting only localized states in the band gaps.