Random matrix analysis of localization properties of gene coexpression network.

@article{Jalan2010RandomMA,
  title={Random matrix analysis of localization properties of gene coexpression network.},
  author={Sarika Jalan and Norbert Solymosi and G{\'a}bor Vattay and Baowen Li},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  year={2010},
  volume={81 4 Pt 2},
  pages={
          046118
        }
}
  • S. Jalan, N. Solymosi, Baowen Li
  • Published 27 January 2010
  • Computer Science
  • Physical review. E, Statistical, nonlinear, and soft matter physics
We analyze gene coexpression network under the random matrix theory framework. The nearest-neighbor spacing distribution of the adjacency matrix of this network follows Gaussian orthogonal statistics of random matrix theory (RMT). Spectral rigidity test follows random matrix prediction for a certain range and deviates afterwards. Eigenvector analysis of the network using inverse participation ratio suggests that the statistics of bulk of the eigenvalues of network is consistent with those of… 
View on PubMed
arxiv.org
39 Citations
Highly Influential Citations
2
Background Citations
8
Methods Citations
5

Figures and Tables from this paper

39 Citations

Citation Type

Citation Type

Spectral analysis of gene co-expression network of Zebrafish
TLDR
Preliminary biological interpretation of the genes, associated with the top contributing nodes in the localized eigenvectors, suggests that the genes corresponding to same vector share common features.
Randomness and Structure in Collaboration Networks: A Random Matrix Analysis
TLDR
It is propagated that a blend of directional advancement and the mixing of schools of thoughts is essential for the steady development of a particular field of research.
Analyzing the heterogeneous structure of the genes interaction network through the random matrix theory
TLDR
This work aims to analyze the structure of the genes interaction network through the random matrix theory on the Pearson Correlation Coefficient network of about 6000 genes of the yeast Saccharomyces cerevisiae, and observes noticeable deviation from a random structure.
Eigenvalue crossing in principal eigenvector localized networks.
TLDR
This work investigates the relationships of the localization properties of PEV with the entire spectra and reports that the localization behavior ofPEV is closely related with that of the second largest eigenvector.
Localization of eigenvectors in random graphs
AbstractUsing exact numerical diagonalization, we investigate localization in two classes of random matrices corresponding to random graphs. The first class comprises the adjacency matrices of…
Information Entropy of Tight-Binding Random Networks with Losses and Gain: Scaling and Universality
TLDR
It is demonstrated that for fixed ξ, the spectral properties (characterized by the position of the eigenvalues on the complex plane) of the network model are also universal; i.e., they do not depend on the specific values of thenetwork parameters.
Application of Random Matrix Theory to Complex Networks
TLDR
Spectral rigidity of spectra provides measure of randomness in underlying networks and potential of RMT framework is provided and obtained to understand and predict behavior of complex systems with underlying network structure.
Normal mode analysis of spectra of random networks
Quantifying randomness in protein–protein interaction networks of different species: A random matrix approach
Jaccard Guided Perturbation for Eigenvector Localization
TLDR
The results show that the proposed JGP approach achieve better PEV localization than the existing RP method, and in scale-free networks, JGP shows a better preservation of scale- free property than that of RP.
...
1
2
3
4
...

References

SHOWING 1-10 OF 92 REFERENCES
Random matrix analysis of complex networks.
TLDR
This work analyzes the eigenvalues of the adjacency matrix of various model networks, namely, random, scale-free, and small-world networks, using nearest-neighbor and next-nearest-NEighbor spacing distributions to probe long-range correlations in the Eigenvalues.
Spectral analysis of deformed random networks.
  • S. Jalan
  • Computer Science
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2009
We study spectral behavior of sparsely connected random networks under the random matrix framework. Subnetworks without any connection among them form a network having perfect community structure. As…
Universality in complex networks: random matrix analysis.
TLDR
It is shown that nearest neighbor spacing distribution of the eigenvalues of the adjacency matrices of various model networks, namely scale-free, small-world, and random networks follow universal Gaussian orthogonal ensemble statistics of random matrix theory.
Spectral analysis and the dynamic response of complex networks.
TLDR
It is shown that the spectral density of hierarchical networks follows a very different pattern, which can be used as a fingerprint of modularity, related to the homeostatic response of the network.
Localizations on Complex Networks
TLDR
The probability distribution function of the components of the representative eigenvectors are proposed to describe the localization on networks where the Euclidean distance is invalid and found that the ascending-order-ranked series of the occurrence probabilities at the nodes behave generally multifractally.
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.
Deformed Gaussian-orthogonal-ensemble description of small-world networks.
TLDR
The analysis performed in this paper proves the utility of the DGOE in network physics, as much as it has been useful in other physical systems.
Laplacian spectra as a diagnostic tool for network structure and dynamics.
TLDR
The effects of clustering, degree distribution, and a particular type of coupling asymmetry (input normalization), all of which are known to have effects on the synchronizability of oscillator networks, are studied.
Constructing gene co-expression networks and predicting functions of unknown genes by random matrix theory
TLDR
The authors' rigorous analysis of gene expression microarray profiles using RMT has showed that the transition of NNSD of correlation matrix of microarray profile provides a profound theoretical criterion to determine the correlation threshold for identifying gene co-expression networks.
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.
...
1
2
3
4
5
...