Computation of Spectra of Large Networks

2010-11-27
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.

Suggestions

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 Design Emergence by Complexity and Morphogenesis
Gürsel Dino, İpek (null; 2016-12-17)
Emergence is the form or behavior of natural or artificial systems, which materializes due to the system components’ interactions with each other and their environment. Emergent properties are a result of processes of self-organization of complex systems such as swarming behavior of birds, insect colonies, immune systems, cities, the World Wide Web, social interactions, etc., as well as processes of natural morphogenesis that exhibit behavior of growth and adaptation. Emergent systems are also closely relat...
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.