Computation of Spectra of Large Networks

Date

2010-11-27

Author

Erdem, Özge
Karasözen, Bülent

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

242
views

0
downloads

Many interacting complex systems in biology, physics, technology and social systems can be represented in a form of large networks. The networks are mathematically represented by graphs. A graph is usually represented by adjacency or Laplacian matrix. Many important features of the underlying structure and dynamics of them can be extracted from the analysis of the spectrum of graphs. Spectral analysis of the so called normalized Laplacian matrix of large networks has become popular in recent years. The Laplacian matrices of empirical networks are in form of unstructured large sparse matrices.

Subject Keywords

Directed and undirected graphs, Laplacian, Krylov methods, Eigenvalues

URI

https://hdl.handle.net/11511/54631

Collections

Department of Basic English, Conference / Seminar

Suggestions

OpenMETU
Core

Computation and analysis of spectra of large undirected networks Erdem, Özge; Karasözen, Bülent; Jost, Jürgen; Department of Scientific Computing (2010) Many interacting complex systems in biology, in physics, in technology and social systems, can be represented in a form of large networks. These large networks are mathematically represented by graphs. A graph is represented usually by the adjacency or the Laplacian matrix. Important features of the underlying structure and dynamics of them can be extracted from the analysis of the spectrum of the graphs. Spectral analysis of the so called normalized Laplacian of large networks became popular in the recent ...
Computation of Graph Spectra of Protein-Protein Interaction Networks Karasözen, Bülent (2011-05-05) Complex systems from many areas such as biology, sociology, technology appear in form of large networks. These networks are represented usually in form of graphs and their structural properties are analyzed using the methods of graph theory. The so called Laplacian matrix became an important tool of spectral graph theory for the investigation of structural properties of large biological networks. Many important features of the underlying structure and dynamics of systems can be extracted from the analysis o...
Computation and analysis of spectra of large networks with directed graphs Sarıaydın, Ayşe; Karasözen, Bülent; Jost, Jürgen; Department of Scientific Computing (2010) Analysis of large networks in biology, science, technology and social systems have become very popular recently. These networks are mathematically represented as graphs. The task is then to extract relevant qualitative information about the empirical networks from the analysis of these graphs. It was found that a graph can be conveniently represented by the spectrum of a suitable difference operator, the normalized graph Laplacian, which underlies diffusions and random walks on graphs. When applied to large...
Evaluating the effects of rescaling parameters in large-scale genomic simulations Kıratlı, Ozan; Birand Özsoy, Ayşegül Ceren; Department of Biology (2016) Computer simulations are widely used in many subdisciplines of biological sciences, which evolutionary biology. Large-scale genomic simulations, where several kb (kilo base) to several Mb (megabase) genomes are modeled, are being increasingly used. These simulations require high computing power. There are some methods proposed in the literature to decrease the time and memory demand of these simulations. This study is concentrated on one of those methods, where both the number of generation, and the number ...
Computational spectral imaging techniques using diffractive lenses and compressive sensing Kar, Oğuzhan Fatih; Öktem, Sevinç Figen; Department of Electrical and Electronics Engineering (2019) Spectral imaging is a fundamental diagnostic technique in physical sciences with application in diverse fields such as physics, chemistry, biology, medicine, astronomy, and remote sensing. In this thesis, we first present a modified version of a high-resolution computational spectral imaging modality and develop a fast sparse recovery method to solve the associated large-scale inverse problems. This technique uses a diffractive lens called photon sieve for dispersing the optical field. We then extend this t...

Citation Formats

Ö. Erdem and B. Karasözen, “Computation of Spectra of Large Networks,” 2010, vol. 1309, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/54631.